Investigation on convective heat transfer behaviour of kerosene-Al2O3 nanofluid

Accepted Manuscript Investigation on Convective Heat Transfer Behavior of Kerosene- Al2O3 Nanofluid Deepak Kumar Agarwal, Aravind Vaidyanathan, S. Sunil Kumar PII:

S1359-4311(15)00278-1

DOI:

10.1016/j.applthermaleng.2015.03.054

Reference:

ATE 6489

To appear in:

Applied Thermal Engineering

Received Date: 29 December 2014 Revised Date:

18 March 2015

Accepted Date: 21 March 2015

Please cite this article as: D.K. Agarwal, A. Vaidyanathan, S Sunil Kumar, Investigation on Convective Heat Transfer Behavior of Kerosene- Al2O3 Nanofluid, Applied Thermal Engineering (2015), doi: 10.1016/j.applthermaleng.2015.03.054. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Investigation on Convective Heat Transfer Behavior of Kerosene- Al2O3 Nanofluid

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Deepak Kumar Agarwala, Aravind Vaidyanathanb, S Sunil Kumara* Liquid Propulsion Systems Centre, ISRO, Thiruvananthapuram, Kerala, India - 695 547,

Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, India - 695

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547, *

Corresponding author. email: [email protected], ph: +91 471 256 7743, fax: +91

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471 256 7039 Abstract

Turbulent convective heat transfer behavior of kerosene- Al2O3 nanofluid is investigated experimentally in horizontal circular test section configuration in a closed loop test setup. The

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study intends to explore the potential use of kerosene- Al2O3 nanofluid for thrust chamber regenerative cooling in semi-cryogenic rocket engine due to its enhanced thermal properties. The effects of variation in particle size (13 nm, 50nm), volume fraction (0.05%, 0.2%, 0.3%,

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and 0.5%) and Reynolds number (6000 – 38000) on convective heat transfer performance and pressure drop are determined using the uniformly heated circular test section. Heat transfer

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performance of nanofluid is evaluated based on identical Reynolds number, Peclet number, velocity and constant pressure drop conditions. Detailed investigation of experimental data shows that in almost all the cases, heat transfer properties of nanofluid are significantly high compared to pure kerosene. Higher heat transfer coefficient is noticed for larger particle size nanofluid compared to smaller size though the measured thermal conductivity is higher for lower particle size nanofluid. A parameter to determine the total heat transfer performance of nanofluid is also defined, which again indicate the thermal advantages of nanofluid as a heat 1

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transfer fluid compared to the base fluid. The experiments also highlight the significant role of Prandtl number in convective heat transfer of nanofluids. A homogeneous fluid correlation which accurately predicts heat transfer coefficient and pressure drop for nanofluids is also

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presented. Keywords: Kerosene, Nanofluid, Reynolds number, convective heat transfer, thermal conductivity, dynamic viscosity

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Nomenclature Specific heat (J/kgK)

Di

Diameter of test section, (m)

f

Friction factor

h

Heat Transfer Coefficient (W/m2K)

I

Current (A)

k

Thermal conductivity (W/mK)

L

Length of test section (m)

Mo

Muoromtseff number

N

Particle count

Nu

Nusselt number

Pe

Peclet number

Pr

Prandtl number

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Cp

Q

Heat energy (W)

Re

Reynolds number 2

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T

Temperature (ºC)

V

Voltage (V)

X

Axial distance along the test section (m)

Greek Symbol Nanoparticle volume concentration (%)

µ

Dynamic Viscosity ( kg/ms)

ρ

Density (kg/m3)

ΔP

Pressure drop (Pa)

c

current value

f

fluid

i

initial value

nf

nanofluid

np

nanoparticle

s

surface

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base fluid

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bf

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Subscripts

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Φ

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Volume flow rate (m3/s)

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1. Introduction Most of the liquid rocket thrust chambers are regeneratively cooled by circulating one of the propellants along the outer surface of the nozzle wall through channels. Heat transfer

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characteristics of such systems mainly depend upon the thermo physical properties of the coolants and their flow velocities. With the addition of small amount of nanoparticles in the

propellant, as referred by Choi [1], thermo physical properties of base fluid can be enhanced.

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Many experimental and theoretical studies carried out [2] clearly indicate higher thermal conductivity and viscosity for nanofluids compared to base fluid. Although increase in

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effective thermal conductivity of fluid is important for its heat transfer performance augmentation, viscosity, specific heat and density are the other factors that affect the heat transfer performance of a fluid in a flowing system.

Over the last one and half decade, several researchers have investigated the convective heat transfer performance of nanofluids under turbulent flow regime. The heat transfer

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performance of water- Al2O3 and water-TiO2 nanofluid was first experimentally investigated by Pak and Cho [3]. They observed 12% decrease in heat transfer coefficient for 3vol% particle concentration of water- Al2O3 nanofluid compared to pure water at identical velocity

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condition. Xuan and Li [4] have theoretically showed that the enhanced convective performance of nanofluid results not only from its enhanced thermal conductivity but also

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from the random movement of particle inside the base fluid and its dispersion effects. Further, Xuan and Li [5] examined the heat transfer performance of water-Cu nanofluid at turbulent flow regime and observed 40% increase in heat transfer coefficient of nanofluid compared to water at the same velocity. They suggested that the relatively low heat transfer performance observed by Pak and Cho [2] might be due to the higher viscosity of their nanofluid compared to water. The measured pressure drop during convective experiments 5

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was very similar to the pure fluid. Contrary to this, experimental study of Ko et al. [6] indicated lower friction factors for water-carbon nano tube nanofluids as compared to pure water for certain ranges of flow rates.

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Yu et al. [7] observed 50-60% enhancement in heat transfer coefficient of 3.7vol% particle concentration water-silicon carbide nanofluid compared to water for identical Reynolds

numbers. However, the heat transfer coefficient of the nanofluid was found to be lower than

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the base fluid when compared for same fluid velocity. They used Mouromtseff number (Mo) to compare the relative performance of water- SiC and water- Al2O3 nanofluid. Mouromtseff

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number is used by many researchers [8, 9] to determine the convective performance of their nanofluid based on the thermo-physical properties measurements.

The research article of Haghigghi et al. [10] reported significant enhancement in heat transfer of their nanofluids at laminar flow regime for identical Reynolds numbers, whereas no significant improvement in heat transfer was noticed when the same was compared for

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identical velocity. Further, based on a theoretical study, Yu et al. [8] concluded that the identical Reynolds number based comparison should not be used for nanofluid study as this type of comparison could alter the flow physics.

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A Peclet number based criterion is used by many researchers [4, 11 and 12] to determine the convective heat transfer performance of their nanofluid. Nasiri et al. [11] investigated the

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heat transfer performance of water based Al2O3 and TiO2 nanofluids in a square channel and found high heat transfer performance for both the nanofluids for identical Peclet number. According to Heris et al. [12], particles fluctuations and interactions, in high Peclet number may cause the change in flow structure and lead to significant augmentation in heat transfer due to presence of nanoparticles.

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The effect of particle size on convective heat transfer performance is evaluated by many researchers [13, 14 and16]. The convective heat transfer experiments carried out by He et al. [13] on water- TiO2 nanofluid with three different particle size did not showed any particle

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size dependency on convective heat transfer. They concluded that the effect of particle concentration is more evident in turbulent flow regime and no additional increment in the

measured pressure drop of nanofluid. Timofeeva et al. [14] investigated the effect of particle size on convective heat transfer coefficient of water-SiC nanofluid. The heat transfer

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coefficient for nanofluids with 16 and 29 nm particle size was found to be lower than that of pure water for identical velocity conditions; however for 66 and 90 nm particle nanofluid,

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heat transfer coefficient was slightly higher than water. The study also indicated that the heat transfer performance of nanofluid was independent of the inlet fluid temperature. Recent study of Sonawane et al. [15] with Aviation Turbine fuel (ATF) - Al2O3 nanofluid also showed increased heat transfer coefficient of nanofluid compared to the ATF alone. In a

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further study conducted by Sonawane et al. [16], it was found that the nanofluids exhibited higher heat transfer performance at elevated temperature. Their experimental investigation show higher heat transfer performance for nanofluid with 150 nm size Al2O3 particles

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compared to 50 nm particle size nanofluid.

Hwang et al. [17] found a good agreement between nanofluid friction factor calculated

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through an analytical method and found the experimental convective heat transfer performance of the nanofluid to be significantly higher compared to the one calculated through analytical models. Based on their scale analysis, the enhanced convection property of nanofluid is due to flattening of velocity profile near the surface, which results in large temperature gradient near the wall. Subsequently based on the experimental study Heyhat et al. [18] found that the single phase correlation was not effective in predicting the convective 7

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performance and pressure drop characteristics of water-Al2O3 nanofluid and the measured pressure drop was about 5.7 times higher than the pure fluid at 2vol% particle concentration of nanoparticle. According to Yu et al. [19], the theoretical correlation works very well for

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nanofluid made using spherical particles whereas it was not effective for case with nanofluid containing rod-like nanoparticles. Experimental study by Williams et al. [20] indicated that conventional correlation of pure fluids with the measured nanofluid properties would accurately reproduce heat transfer performance and pressure drop characteristics in

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nanofluids. Subsequently, Rea at al. [21] also observed that the convective heat transfer

property and pressure drop characteristics of nanofluid can be accurately predicted by means

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of the traditional correlations provided the effective nanofluid properties are incorporated in the calculations.

Many researchers [2, 22-24] have clearly reported higher heat transfer performance for nanofluid as compared to the base fluid alone. The degree of enhancement clearly depends

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not only on the nanoparticle size and its combination with base fluid but also on the type of comparison method used by the researchers. In a previous research work, the authors [25] clearly indicated the close dependence of the method of synthesis of kerosene- Al2O3

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nanofluid over its own stability. Significant improvement in thermal conductivity of kerosene- Al2O3 nanofluid was observed by them which could lead to enhanced convective

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heat transfer of these nanofluids.

In the present study, detailed experimental investigation is carried out with kerosene- Al2O3 nanofluid to assess its potential heat transfer application in thrust chamber cooling of liquid rocket engine. The study includes measurement of thermo-physical properties and subsequent determination of heat transfer performance by conducting a series of convective heat transfer experiments in a closed loop experimental test setup for a range of Reynolds numbers. The 8

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current study explores the effect of particle size on heat transfer performance of nanofluid. A detailed analysis of the experimentally generated data is carried out to gain further insight into the convective heat transfer performance of kerosene- Al2O3 nanofluid with respect to

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that of pure fluid based on identical Reynolds number, Peclet number and flow velocity. 2. Experimental Techniques 2.1. Measurements of properties

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In the present work, both thermal conductivity and dynamic viscosity of nanofluids is measured under static condition. The thermal conductivity is measured using thermal

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property analyser named KD2-Pro, which works on the principle of transient hot wire method with a specified accuracy of ±5%. The dynamic viscosity is measured using Brookfield LVDV-II digital viscometer with cone type spindle. The rotation of spindle in viscosity measurement is kept at 100 rpm, which gives the maximum viscosity measurement range of 3.04 cP. The maximum error specified for the equipment is 1% of the maximum

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measurement range ie; 0.03 cP for the present measurement setup. The measurement procedure given in Deepak et al. [25] is followed in the current study.

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2.2. Experimental setup

The schematic of the closed loop convective heat transfer experimental setup is shown in Fig.

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1. The experimental setup consists of a test section, resistively heated by a DC power source, nanofluid ultrasonication unit, variable flow gear pump, turbine flow meter, heat exchanger, a differential pressure indicator and data acquisition system. The test section is made up of 1.2m long stainless steel tube having 9.5 mm outer diameter with 0.9 mm thickness. Ten Ttype thermocouples are welded on to the test section for measuring the surface temperatures and two T-type thermocouples each are positioned at the inlet and outlet of the test section respectively for measuring the respective fluid temperatures. Experiments are carried out in 9

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turbulent flow regime. The entrance length (X) for fully developed flow [26] in turbulent regime can be defined as; (1)

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X ≥ 10Di

Di is the internal diameter of the test section. From the above equation the minimum entrance length calculated is 0.077 m. It is to be noted that in the test setup, tube diameter is constant everywhere and before starting of test section, a calm length of 0.2 m is given for flow to

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become hydrodynamically developed. An entrance length of 0.5m, (X /Di = 65) in the test section is used before making the surface temperature measurements to compute the heat

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transfer coefficient to ensure fully developed thermal and flow profile for the measurements. The test section is insulated with glass wool to reduce the heat loss to the ambient. Thermal properties of kerosene and Al2O3 used in the current study are given in Table 1. 2.3. Experimental procedure Nanofluid preparation

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2.3.1.

Uniform dispersion of nanoparticle in the base fluid is an important requirement for any colloidal system to be effectively used for heat transfer application. In the present

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investigation, nanofluids are prepared using two-step technique with two nominal particle sizes, 13 nm and 50 nm. Various surfactants and ultrasonication techniques are tried to

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stabilize nanofluid. Oleic acid as a surfactant is found to be suitable for preventing particle agglomeration in the nanofluid. Based on the numerous trials, surfactant to particle volume ratio of 0.3 and disruptor type ultrasonicator [25] with 20 KHz, 500 W power levels is chosen for the preparation of nanofluid. The nanofluid thus prepared is visually inspected for more than 10 days and no major particle settling is noticed. Different ultrasonication time of 30 minutes for 0.05 % particle volume fraction to 3hrs for 1% particle volume fraction is used. 10

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The stability of nanofluids is found to be directly related to the concentration of the nanoparticles. Nanofluids at lower volume fraction less than 0.2% are visually found to be very stable as compared to those with higher particle concentration. Heat transfer performance

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2.3.2.

Nanofluid of desired particle volume concentration and quantity is prepared using oleic acid as surfactant and is filled in the nanofluid reservoir. The nanofluid kept in the reservoir is

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continuously ultrasonicated with the help of ultrasonic probe, flow cell and peristaltic pump.

Before starting the convective heat transfer experiment, thermal conductivity and viscosity of

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nanofluid is measured using KD2 pro and Brookfield viscometer respectively. During the measurement of properties, sample is kept at a constant temperature using a constant temperature bath. Thermo physical properties are determined at various temperatures from 25ºC to 75ºC for each volume fraction and particle size. A variable type gear pump delivers the desired volume flow of nanofluid to the test section through a turbine type flow meter that

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measures the flow rate during the experimental run with an accuracy of ± 0.25%. The test section is resistively heated using a variable high current DC power source of 20 kW. The differential pressure indicator with a differential pressure range of 500 mbar measures the

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pressure drop across the test section. A 30 channel data acquisition system records all the surface temperatures, inlet and outlet fluid temperature, flow rate and deferential pressure

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during the test. The hot nanofluid from the test section enters to water cooled plate heat exchanger which has cooling capacity of 20 kW. Temperature of nanofluid at the outlet of heat exchanger is same as the ambient and collected back in to the reservoir. The process continued until steady state attains. The inlet fluid temperature to the test section is maintained constant during the test. The experiments are carried out for different Reynolds

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number by varying the volume flow rate and each test is repeated four times to ensure repeatability. After each test, the fluid lines are purged initially with nitrogen gas to avoid adhesion of

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nanoparticles to the inner surfaces of the pipelines and the equipments. Subsequently, purging is done with isopropyl alcohol to remove kerosene. 2.4. Uncertainty and Data reduction

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A series of experiments are carried out to investigate heat transfer characteristics of nanofluid at turbulent flow regime. Steady state fluid temperature, surface temperature, current and

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voltage from DC power source and flow rate are measured during the experiment for calculating heat transfer coefficient and Nusselt number at various particle volume concentrations and Reynolds numbers. Thermal conductivity and viscosity measured at various temperatures are curve-fitted to piecewise liner to evaluate the values at any

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temperature point. The effective density and specific heat of nanofluid are estimated based on the physical principle of the mixture rules as follows; ρnf = Φ ρnp + (1- Φ) ρbf

(3)

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Cpnf = (Φ ρnpCpnp + (1- Φ) ρbfCpbf)/ρnf

(2)

The density and specific heat for kerosene are 809 kg/m3 and 2093 J/kg K respectively and

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that of Al2O3 nanoparticle are 3920 kg/m3 and 773 J/kg K respectively at 25 ⁰C. Heat absorbed by the nanofluid in test section is calculated by Qf = ρnf

nfCpnf

(Tout-Tin)

(4)

Electrical heat supplied to the test section Qe is given as, Qe = V I

(5) 12

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As the value of specific heat of nanofluid is calculated by mixing rule, the correctness of specific heat is ensured by comparing heat absorbed by the nanofluid, Qf in test section to the electrical heat supplied, Qe to test section. In all the experiments (Qe - Qf) is found to be

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positive and the value is less than 7.2% and this indicated the effectiveness of the insulation provided on the test section. Reynolds number and Prandtl number of nanofluid is determined using the expressions nfDi

/ πDi2µ nf

(6)

Prnf = µ nf Cpnf / knf

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Local Heat transfer coefficient, hnf = Qf/ (πDi L (Ts -Tf))

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Renf =4ρnf

Where,

(7) (8)

Ts and Tf are the local surface and fluid temperature respectively. Tf = Tin + x/L(Tout -Tin)

(9) (10)

Friction factor, f = 2∆pDi/(ρnf Lu2nf)

(11)

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Nusselt Number Nunf = hnfDi/knf

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Where, ∆p is the measured pressure drop. Peclet Number, Pe = Re Pr

(12)

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An uncertainty analysis of the experimental data is carried out and the maximum uncertainty in all important parameters is presented in Table 2. 3. Results and discussion The detailed experimental investigation involves determination of thermo physical and convective heat transfer properties of kerosene- Al2O3 nanofluid at different particle volume fraction for particle sizes of 13nm and 50nm. Total heat transfer performance of these 13

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nanofluids is evaluated by measuring the pressure drop in the test section during each test. Detailed discussion related to the results obtained in each step is summarized in following paragraphs.

3.1.1.

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3.1. Thermo-physical properties Thermal Conductivity

Detailed measurements of thermal conductivity and viscosity are made at 0.05%, 0.1%,

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0.2%, 0.3% and 0.5% volume fractions of Al2O3 nanoparticles in kerosene and presented by the authors [25]. Figure 2 shows the ratio of thermal conductivity of kerosene- Al2O3

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nanofluid to kerosene at various particle volume concentrations and fluid temperatures for the two different particle sizes of 13nm and 50nm. It is seen from the figure that the ratio of thermal conductivity of nanofluid to base fluid increases with particle loading and temperature for both nanoparticle sizes. The ratio of thermal conductivity of nanofluid to base fluid is found to be higher for the smaller sized particle compared to the bigger sized

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particle for a range of particle concentrations.

Strong temperature dependency on thermal conductivity of nanofluid is observed from Fig. 2.

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Higher percentage enhancement in thermal conductivity is noticed for lower particle size nanofluids at every temperature range. As already discussed by Deepak et al. [25], this could

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be attributed to the higher degree of Brownian motion that exist at lower particle size compared to larger particle size in the base fluid. 3.1.2.

Dynamic Viscosity

Ratio of dynamic viscosity of nanofluids to the base fluid at various fluid temperatures and particle concentrations for 13 and 50 nm particle size nanofluids is presented in Fig. 3. It is seen from the figure that the dynamic viscosity of nanofluid is higher compared to the base fluid and the enhancement in viscosity increases with particle loading and fluid temperature. 14

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The increase in dynamic viscosity for smaller particle size is large when compared to that of the bigger particles. This could be due to the availability of higher surface area in the case of the smaller size particle with respect to the bigger size particle at same volume concentration.

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This led to higher interfacial resistance with the fluid layer and result in increased viscosity for smaller particle size nanofluid. It is also observed that the ratio of dynamic viscosity increases with temperature for both the nanofluids. This could be due to the increased

Brownian motion of nanoparticles at elevated temperature that caused increased internal

3.2. Convective Heat Transfer

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temperature for both the particle sizes of nanofluid.

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resistance in the flow and resulted in higher percentage enhancement in viscosity at elevated

The convective heat transfer performance of any fluid depends upon various physical and thermo-physical properties. Though the enhanced thermal conductivity of nanofluid will result in reduced resistance to thermal diffusion in the laminar sub layer, increased viscosity

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of nanofluid could increase the thickness of sub layer and in turn increase the thermal resistance to heat transfer.

Test setup validation

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3.2.1.

Before carrying out the convective heat transfer experiments with nanofluid, the

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experimental test setup and the operational procedure is validated by experimentally evaluating convective heat transfer data, and comparing it with the available correlations from the literature for pure kerosene. Figure 4 shows the comparison of heat transfer coefficient determined from the current experiments and those calculated based on the wellknown Dittus-Bolter correlation [26] for turbulent flow regime. Nu = 0.023Re0.8 Pr0.4

(13)

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Good agreement is seen between the experimental data and the correlation which confirms the reliability of the experimental data obtained from the current test setup. 3.2.2.

Mouromtseff number (Mo)

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To compare the fluid property related heat transfer performance of a nanofluid to that of a

base fluid in a given geometry at a fixed velocity, Mouromtseff number (Mo)) is used. The fluid with larger value of Mo is considered to be a better coolant than the others [7-9].

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Mouromtseff number is expressed as

(14)

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Mo = (hnf/hbf) = (ρnf/ρbf)4/5(Cpnf/Cpbf)2/5(µnf/µbf)-2/5(knf/kbf)3/5

Figure 5 shows the Mouromtseff number calculated for 13nm and 50 nm particle size kerosene- Al2O3 nanofluid at various particle concentrations. It can be observed that at all particle concentrations and for both particle size, the Mo number is greater than unity and this clearly indicates higher heat transfer performance of the current kerosene- Al2O3

3.2.3.

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nanofluids over the pure kerosene.

Convective heat transfer Coefficient

Subsequent to the validation of the experimental setup, detailed convective heat transfer

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study of nanofluid is carried out for 0.05%, 0.2%, 0.3% and 0.5% particle volume concentrations of the nanofluid. Effect of particle size on heat transfer is also studied

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experimentally for 13nm and 50nm particle size nanofluids. Thermo physical properties at average film temperature ((Ts+Tf)/2) is used for the computation of heat transfer coefficient from the experimental data. Each experiment is repeated four times and the mean values are used for subsequent analysis. The maximum dispersion in the calculated heat transfer coefficients among the experiments for any particular case is within 3.8%. Heat transfer

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coefficient for 13 nm and 50 nm particle nanofluids derived from the experimental data at various particle concentrations and Reynolds number is presented in Fig. 6. It can be clearly seen that kerosene- Al2O3 nanofluid shows enhanced heat transfer properties

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as compared to the pure kerosene at all Reynolds number range. As expected, the heat transfer coefficient of kerosene- Al2O3 nanofluid is found to increase with Reynolds number and particle volume concentrations. In contrast to lower value of thermal conductivity of

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bigger size particle nanofluid, the measured heat transfer coefficient is observed to be higher for bigger sized particle nanofluid as compared to the smaller sized particle nanofluids. As

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already discussed, higher thermal conductivity observed for small size particle nanofluid could be attributed to the higher Brownian motion as compared to the bigger particle in a stagnant fluid [25]; however this need not be true for the nanofluid in a turbulent flow regime. In the turbulent flow regime, the effect of Brownian motion will be inferior to the effect caused due to the very high velocity of the fluid. One of the possible reason for the

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enhanced thermal conductivity of nanofluid due to mechanisms other than Brownian motion can be the reduction in thermal diffusion resistance in the laminar sub layer of the boundary layer which can result in higher heat transfer performance of the nanofluid compared to the

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base fluid. The higher viscosity observed for smaller sized particle nanofluid, leads to increased thickness of laminar sub layer of the momentum boundary layer and in turn

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increases its resistance to heat transfer. This combined effect of thermo physical properties along with the effect of higher disruption in the sub layer by bigger sized particles can result in higher heat transfer performance. Heat transfer coefficient at 0.3% volume fraction of 50nm sized particle is compared with Sonawane et al. [16] and shown in Fig. 7 as the properties of ATF and kerosene are very close. Test setup and parameters used by them is defined in Sonawane et al. [16]. Figure 7 shows well comparison of present experimental data with Sonawane et al. [16]. 17

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As discussed by the Pak and Cho [3], comparing heat transfer performance of nanofluid to its base fluid at identical Reynolds number is not the best approach. Higher viscosity of nanofluids requires higher velocity to achieve the same Reynolds number and an identical

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velocity based comparison rather than identical Reynolds number based assessment is more appropriate for determining the heat transfer performance of nanofluids. Keeping this in

mind, the heat transfer performance comparison of various kerosene- Al2O3 nanofluids at

different flow velocity is carried out and the results are presented in Fig. 8. As expected the

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measured heat transfer coefficient increases with flow velocities. It can be seen that similar to the Reynolds number comparison, the heat transfer performance of current nanofluids are

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significantly higher compared to the base fluid for identical velocity conditions as well. However, the magnitude of the enhancement in heat transfer coefficient is found to be lower in the case of velocity based analysis as compared to those based on identical Reynolds number.

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A Peclet number based criterion has been used by many researchers [4, 11 and 12] for the comparison of heat transfer performance of nanofluid. The Peclet number describes the effect of thermal dispersion induced by micro-convection and micro-diffusion of nanoparticles.

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Figure 9 shows the heat transfer coefficient of various nanofluid based on the Peclet number. The higher heat transfer coefficient of nanofluid as compared to the base fluid, indicates,

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significant effect of micro convection and micro diffusion along with the particle migration and clustering effects.

Figures 10 -12 shows the ratio of heat transfer coefficient of nanofluid to its base fluid at various particle concentration and sizes based on Reynolds number, constant flow velocity and Peclet number respectively. The maximum enhancement observed in the present investigation is 1.69, 1.41 and 1.59 based on identical Reynolds number, velocity and Peclet 18

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number based criteria respectively for 50 nm, 0.5% volume concentration nanofluid. The enhancement ratio obtained based on the velocity criteria is lowest as compared to the others. Contradictory to Pak and Cho [3], and Yu et al. [8], the current investigation shows

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enhancement ratio greater than one in all the cases when compared with the velocity based criteria. This could be attributed to the marginal increase in viscosity observed in the present investigation as compared to the significant increase in viscosity observed by Pak and Cho

transfer coefficient for identical flow velocity magnitudes. Pressure drop and friction factor

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3.2.4.

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[3] and Yu et al. [8] in their nanofluid wherein the authors had observed decrease in heat

Though the current investigation shows enhanced heat transfer performance of the keroseneAl2O3 nanofluid, due to the increased viscosity of nanofluids it is expected that the system of flowing nanofluid will have higher pressure drop. Higher pressure drop may limit nanofluid applicability in thrust chamber cooling as it may require a bigger pump to push the fluid

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though the regenerative passage in thrust chamber. The pressure drop in the flow of pure kerosene in the test section is measured using differential pressure gauge. The comparison of measured pressure drop of pure kerosene at

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various Reynolds number to the pressure drop computed using Blasius and McAdams

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correlation [26] is shown in Fig. 13. f = 0.316 Re-0.25

(15)

f = 0.184 Re-0.2

(16)

The experimental results obtained in the current study are seen to be in good agreement with the values predicted based on the correlation.

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The friction factor for kerosene- Al2O3 nanofluid at various particle concentration and sizes is computed from the measured pressure drop. Figure 14 shows the variation of friction factor calculated in the present study, along with the correlation provided by Sonawane et al.

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[16] for ATF+ Al2O3 nanofluid, and those obtained from Blasius correlation. It is seen that a homogeneous fluid correlation is sufficient enough to accurately predict pressure drop

characteristics of the nanofluids used in the current study. Correlation for friction factor is

f = 0.255Re-0.22

(17)

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Valid over a range of Re 6000 to 40000.

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obtained in present study by curve fitting all the data points and is expressed as;

It can be noted that the maximum dispersion in the friction factor from the above correlation is within 12% and it can be used for the determination of pressure drop in a flowing system of kerosene- Al2O3 nanofluid in liquid rocket engine. Total Heat Transfer Performance

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3.2.5.

The total heat transfer performance of kerosene- Al2O3 nanofluid is determined by comparing the heat transfer augmentation of nanofluid to the pressure penalty due to increased density

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and the viscosity of nanofluid. Ratio of heat transfer enhancement to the increase in pressure drop, i.e. (hnf/hbf)/(∆Pnf/∆Pbf) is used as a parameter to define total heat transfer performance

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of kerosene- Al2O3 nanofluid. This parameter is named as a Merit parameter and is used by Yu et al. [8] for evaluating the total heat transfer performance of water- SiC and water- Al2O3 nanofluid.

Figures 15 and 16 show the heat transfer performance of nanofluid based on merit number with respect to Reynolds number and Peclet number respectively. It can be seen that in most of the cases Merit number is above unity and this indicates that the nanofluid has the potential to substitute base fluid as an effective coolant in various heat transfer applications. 20

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In very few cases of nanofluid with particle volume fraction of 0.05%, Merit number is found to be lower than one. The maximum merit number for 50nm 0.5% volume concentration nanofluid is 1.46 and 1.36 respectively for identical Reynolds number and Peclet number.

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The merit number distribution for identical velocity condition is shown in Fig.17. It can be observed that while using the identical velocity for comparing the total heat transfer

performance of nanofluid to the base fluid, the Merit number is lower as compared to the

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other two criteria. It is seen that nanofluid made up of 0.2% particle volume concentration and above yields Merit number more than unity suggesting the total heat transfer

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performance of these nanofluids to be higher than that of pure kerosene and can be used as a better coolant in regenerative passage of semi-cryo thrust chamber. 3.2.6.

Nusselt number

The variation in Nusselt number of kerosene- Al2O3 nanofluid at various particle volume fractions with Reynolds number is shown in Fig. 18. The computed Nusselt number is

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compared with single phase correlation of Dittus-Boelter [26], and also with the correlation developed by Sonawane et al [16]. It is to be noted that the fluid properties used in DittusBoelter correlation are for the nanofluid at 0.5% particle concentration and 50nm particle

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size. It can be noted that the experimental value of Nusselt number do not compare well with both the correlations. In this regard regression analysis of the test data obtained from the

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present study is attempted and a new correlation is derived as; Nu = 0.005Re0.8Pr

(18)

Valid over a range of Re 6000 to 40000 and Pr 14 to 17. It can be observed that in the present correlation exponent of Prandtl number has increased from 0.4 as in Dittus- Boelter correlation to 1 in the current study. Correlation developed by Sonawane et al [16] and Pak and Choi [3] also reported increased exponent for Prandtl 21

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number. This increase in exponent of Prandtl number indicates the significant role of Prandtl number in nanofluid convective heat transfer process. As discussed in section 3.2.3, the enhancement in convective heat transfer properties of nanofluid could be due to the combined

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effect of change in thermo physical properties, Brownian motion and disturbance in boundary layer thickness. All the experimental data shown in Fig. 18, lies within ±20% of the present

correlation. It is true that the effect of nanoparticle concentration and diameter plays a role in nanofluid convective heat transfer process. However, the aim of presenting the correlation is

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to suggest that the homogeneous fluid correlation with the actual thermo-physical properties of nanofluid could reasonably predict the heat transfer behaviour of nanofluid under

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investigation. 4. Conclusion

Experimental investigation of convective heat transfer performance of kerosene- Al2O3 nanofluids at turbulent flow regime for 13 and 50 nm particle sizes is carried out to determine

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its potential use in regenerative cooling channel of semi cryogenic engine. Though the measurements conforms greater enhancement in thermal conductivity and viscosity for smaller sized nanoparticle fluid, the convective heat transfer experiments indicates lower heat

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transfer performance of these nanofluids compared to bigger sized particle nanofluids. The reason for such behaviour could be attributed to the combined effect of enhanced thermo-

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physical properties and increased disruption in the sub layer by bigger sized particles resulting higher convective heat transfer performance. Convective heat transfer performance of these nanofluids at identical Reynolds number, velocity and Peclet number are compared. Results indicate enhanced heat transfer performance of nanofluid for all these criteria. The maximum enhancement ratio observed is 1.69, 1.41 and 1.59 for identical Reynolds number, velocity and Peclet number respectively 22

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for 50nm and 0.5% volume concentration nanofluid. Due to increased dynamic viscosity of these nanofluids, the enhancement noticed is lowest for identical velocity based criteria. Correlations for friction factor and Nusselt number are developed based on the experimental

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data. The study shows the significant role of Prandtl number in convective heat transfer process in nanofluids.

Merit number, which is a ratio of heat transfer enhancement to the increase in pressure drop,

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is used as a parameter to define total heat transfer performance of nanofluid and a value greater than unity indicates higher total heat transfer performance. Detailed analysis of

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convective heat transfer and measured pressure data shows Merit number above unity for nanofluids with particle concentration above 0.2%, indicating its potential as a suitable heat transfer fluid. The study concludes the utility of kerosene- Al2O3 nanofluids, with particle volume fraction greater than 0.2 % as a potential heat transfer fluid in regenerative cooling of

Acknowledgements

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semi-cryogenic rocket engine.

The authors acknowledge the help of Mr. Jophy Peter, Scientist 'SC', Thermal Engineering

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Division, LPSC, ISRO, Trivandrum in setting up measurement facilities for the

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experimentations.

23

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References: [1]

Choi, S. U. S., Eastman, J. A., 1995. Enhancing thermal conductivity of fluids with nanoparticles,

Report

submitted

to

Argnone

National

Laboratory,

Illinous,

[2]

Das, S. K., Choi, S. U. S., Yu, W., Pradeep T., 2008. Nanofluids-Science and Technology, USA, John Wiley & Sons. 1-37.

Pak, B. C., Cho, Y. I., 1998. Hydrodynamic and heat transfer study of dispersed fluids

SC

[3]

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ANL/MSD/CP-84938.

with submicron metallic oxide particles, Experimental Heat Transfer an International

[4]

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Journal, 11(2), 151-170.

Xuan, Y., Li, Q., 2000. Heat Transfer enhancement of nanofluids, International Journal of Heat and fluid flow, Vol.21, 58-64.

[5]

Xuan, Y., Li, Q., 2003. Investigation on convective Heat Transfer and Flow Features of Nanofluids, Journal of Heat Transfer, Vol.125, 151.

Ko G. H., Heo K., Lee K., Kim D. S., Kim C.,Sohn Y., Choi M., 2007. An experimental

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[6]

study on the pressure drop of nanofluids containing carbon nanotube in a horizontal tube, International Journal of Heat and Mass Transfer 50, 4749-4753. Yu, W., France, David M., Smith, David S., Singh, D., Timofeeva, Elena V., Routbort,

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[7]

Jules L., 2009. Heat transfer to a silicon carbide/water nanofluid, International Journal

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of Heat and Mass Transfer 52, 3606-3612. [8]

Yu, W., France, D. M., Timofeeva, E. V., Singh, D., & Routbort, J. L. (2010). Thermophysical property-related comparison criteria for nanofluid heat transfer enhancement in turbulent flow. Applied Physics Letters, 96(21), 213109.

[9]

Timofeeva, E. V., Yu, W., France, D. M., Singh, D., & Routbort, J. L. (2011). Nanofluids for heat transfer: an engineering approach. Nanoscale research letters, 6(1), 1-7.

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[10] Haghighi, E. B., Saleemi, M., Nikkam, N., Anwar, Z., Lumbreras, I., Behi, M., ... & Palm, B. (2013). Cooling performance of nanofluids in a small diameter tube. Experimental Thermal and Fluid Science, 49, 114-122.

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[11] Nasiri, M., Etemad, S. G.,Bagheri, R., 2011.Turbulent convective heat transfer of nanofluids through a square channel. Korean Journal of Chemical Engineering, 28(12), 2230-2235.

[12] Heris S. Z., Esfahany M. N., Etemad S. G., 2007. Experimental investigation of

of Heat and fluid flow 28, 203-210.

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convective heat transfer of Al2O3/water nanofluid in circular tube, International Journal

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[13] He, Y., Jin, Yi., Chen, H., Ding, Y., Cang, D., Lu, H., 2007. Heat transfer and flow behaviour of aqueous suspensions of TiO2 nanoparticles (nanofluids) flowing upward through a vertical pipe, International Journal of Heat and Mass Transfer 50, 22722281.

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[14] Timofeeva, Elena V., Smith, David S., Yu, Wenhua., France, David M., Singh, D., Routbort, Jules L., 2010. Particle size and interfacial effects on thermo-physical and heat transfer characteristics of water-based α-SiC nanofluids, Nanotechnology 21, 215-

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703.

[15] Sonawane, S., Patankar, K., Fogla, A., Puranik, B., Bhandarkar, U., Kumar, S. Sunil,

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2011. An Experimental investigation of thermo-physical properties and heat transfer performance of Al2O3- Aviation Turbine Fuel nanofluids, Applied Thermal Engineering 31, 2841-2849.

[16] Sonawane, S., Bhandarkar, U., Puranik, B., Kumar, S. Sunil, 2012.Convective Heat Transfer Characterization of Aviation Turbine Fuel-Metal Oxide Nanofluids, Journal of Thermophysics and Heat Transfer Vol.26, No.4.

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[17] Hwang K. S., Jang S. P., Choi S. U. S., 2009. Flow and convective heat transfer characteristics of water-based Al2O3 nanofluids in fully developed laminar flow regime, International Journal of Heat and Mass Transfer 52, 193-199.

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[18] Heyhat M. M., Kowsary F., Rashidi A. M., Momenpour M.H., Amrollahi A., 2013. Experimental investigation of laminar convective heat transfer and pressure drop of water-based Al2O3 nanofluids in fully devloped flow regime, Experimental thermal and Fluid Science, 44, 483-489.

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[19] Yu, L., Liu, D., & Botz, F. (2012). Laminar convective heat transfer of aluminapolyalphaolefin nanofluids containing spherical and non-spherical nanoparticles. Experimental

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Thermal and Fluid Science, 37, 72-83.

[20] Williams, W., Buongiorno, J., Hu, Lin-Wen, 2008.Experimental Investigation of Turbulent Convective Heat Transfer and Pressure Loss of alumina/Water and Zirconia/Water Nanoparticle Colloids (Nanofluids) in Horizontal Tubes, Journal of

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Heat Transfer Vol.130, 042412-1.

[21] Rea U., McKrellt., Hu Lin-wen, Buongiorno J., 2009. Laminar convective heat transfer and viscous pressure loss of alumina-water and zirconia-water nanofluids, International Journal of Heat and Mass Transfer 52, 2442-2448.

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[22] Das, S. K., Choi, S. U. S., Patel, Hrishikesh E., 2006. Heat Transfer in Nanofluid- A

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Review, Heat Transfer Engineering, 27:10, 3-19. [23] Wang, Xiang-Qi, Mujumdar, A. S., 2008. A review on nanofluids - part II: experiments and applications, Brazilian Journal of Chemical Engineering 25 (4).

[24] Kakaç, S.,Pramuanjaroenkij, A., 2009. Review of convective heat transfer enhancement with nanofluids. International Journal of Heat and Mass Transfer, 52(13), 3187-3196. [25] Agarwal D. K., Vaidynathan A., Sunil Kumar S., 2013. Synthesis and characterization of kerosene-alumina nanofluids, Applied Thermal Engineering, 60 275-284. 26

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[26] Incropera Frank P., DeWitt David P., 2011, Fundamental of heat and mass transfer,

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USA, John Wiley & Sons. Ed 7.

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List of figures Schematic of convective heat transfer setup.

Figure 2

Ratio of thermal conductivity of nanofluid to base fluid for various conditions.

Figure 3

Ratio of dynamic viscosity of nanofluid to base fluid for various conditions.

Figure 4

Experimental setup validation with pure kerosene

Figure 5

Mouromtseff number for kerosene- Al2O3 nanofluid at various particle concentration

Variation in convective heat transfer coefficient with Reynolds number for

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Figure 6

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Figure 1

Figure 7

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various particle size and particle volume concentration.

Comparison of convective heat transfer coefficient of 50nm 0.3% particle volume concentration kerosene- Al2O3 nanofluid with Sonawane et al. [16]

Figure 8

Variation in convective heat transfer coefficient with fluid velocity at various particle size and particle volume concentration.

Variation in convective heat transfer coefficient with Peclet number at various

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Figure 9

particle size and particle volume concentration. Figure 10

Variation in ratio of heat transfer coefficient of nanofluid to base fluid with

Figure 11

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Reynolds number for various particle concentration. Variation in ratio of heat transfer coefficient of nanofluid to base fluid with

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fluid velocity at various particle concentration. Figure 12

Variation in ratio of heat transfer coefficient of nanofluid to base fluid with Peclet number for various particle concentration.

Figure 13

Comparison of pressure drop characteristic of pure kerosene with Literature correlations.

Figure 14

Variation in friction factor of nanofluids with Reynolds number at various particle concentrations. 28

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Figure 15

Variation in Merit number with Reynolds number for various particle concentrations of nanofluids.

Figure 16

Variation in Merit number with flow velocity for various particle

Figure 17

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concentrations of nanofluids. Variation in Merit number with Peclet number for various particle concentrations of nanofluids. Figure 18

Variation in Nusselt number of nanofluids with Reynolds number at various

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particle concentrations.

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List of Tables Thermal properties of kerosene and Al2O3

Table 2

Maximum uncertainty in experimental parameters

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Table 1

29

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Table 1 Cp (J/kgK) 2093 773

k(w/mk) 0.104 40

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Kerosene Al2O3

ρ (kg/m3) 809 3920

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Table 2 Maximum Uncertainty (%)

k

5

µ

4

Re

4.9

Pr

7.1

h

6.8

Nu

8.6

Pe

9.4

∆P

5

f

5.2

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Parameter

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400

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350 300

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200

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Nu

250

150 100

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50

Experiment Dittus-Boelter equation

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0

0

10000

20000

30000

Re

40000

50000

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0.80 1.29 1.80 2.23 2.66 3.07 3.42 3.97 4.58 Vel 0.70 1.26 1.56 2.31 2.75 3.18 3.28 4.03 4.73

H 329.594 679.478 1183.04 1636.336 2059.792 2462.359 2849.026 3222.952 3586.306 3940.664 4287.216 4626.894 4960.442 5288.47 5611.485 5929.914 6244.122 888.0548 1536.526 1841.624 2463.771 2424.544 2806.421 3320.008 3641.717 4097.511 #VALUE! 888.0548 1447.366 1894.37 2244.16 2586.982 2904.682 3165.46 3561.468 3994.658 #VALUE! 891.291 1425.054 1690.124 2312.586 2655.211 2981.576 3059.105 3605.963 4104.4

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Nu 24.17023 50.30751 87.59046 121.1518 152.5038 182.3093 210.9375 238.6224 265.5246 291.7607 317.4189 342.5681 367.2635 391.5502 415.4657 439.0417 462.3052 65.75021 113.762 136.351 182.4138 179.5095 207.7831 245.8083 269.6272 303.3734 #VALUE! 65.75021 107.1607 140.2562 166.1542 191.5361 215.0582 234.3658 263.6856 295.7584 #VALUE! 65.98982 105.5088 125.1342 171.2203 196.5877 220.7513 226.4915 266.9799 303.8835

SC

Pe 23304.19 58260.47 116520.9 174781.4 233041.9 291302.3 349562.8 407823.3 466083.8 524344.2 582604.7 640865.2 699125.6 757386.1 815646.6 873907 932167.5 81415 161558.4 202607.8 291511.2 285721 343040.8 423232.1 475102.7 550560.2 #VALUE! 81415 149926.2 209887.1 259401.3 309846.4 358119.5 398750 462052.1 533340.2 #VALUE! 81786.03 147042.8 181992.3 269325.2 320094.7 370008.8 382074.3 469279.1 551717.6

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15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

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Vel

Re Pr 1536.202 3840.506 7681.011 11521.52 15362.02 19202.53 23043.03 26883.54 30724.04 34564.55 38405.06 42245.56 46086.07 49926.57 53767.08 57607.58 61448.09 5366.843 10649.86 13355.82 19216.29 18834.61 22613.1 27899.28 31318.57 36292.7 #VALUE! 5366.843 9883.071 13835.67 17099.62 20424.94 23607.08 26285.43 30458.28 35157.56 #VALUE! 5391.301 9692.999 11996.86 17753.8 21100.51 24390.82 25186.17 30934.68 36368.99

EP

0.20 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 0.70 1.39 1.74 2.50 2.45 2.94 3.63 4.08 4.72

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V

#VALUE! 948.068 1494.933 1849.591 2302.415 2485.954 2743.895 2933.17 3570.648 3966.328 #VALUE! 808.6815 1441.913 1677.676 2131.788 2409.405 2731.215 3182.288 3675.899 4093.567 #VALUE! 880.739 1401.932 1848.404 2204.555 2460.67 2780.331 3225.505 3697.252 4162.99 939.1149 1287.928 1706.285 2032.511 2382.44 2922.599 3348.653 3729.974 4048.468 957.4169 1463.412 1937.89 2309.62 2475.124 2925.775 3198.882 3539.858

SC

#VALUE! 70.1935 110.6826 136.9409 170.4673 184.0562 203.1538 217.1674 264.3653 293.6608 #VALUE! 59.87353 106.7571 124.2126 157.8343 178.3886 202.215 235.6117 272.1579 303.0814 #VALUE! 65.20856 103.7969 136.853 163.2219 182.1842 205.8514 238.8114 273.7388 308.2214 69.53063 95.35623 126.3307 150.484 176.3922 216.3847 247.9291 276.1615 299.7424 70.88568 108.3488 143.4784 171.0007 183.2544 216.6199 236.8403 262.0856

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#VALUE! 88349.5 156110.4 203703.9 267845.4 294795.7 333514.1 362515.3 463541.5 528616.3 #VALUE! 72423.01 149220.6 180318.3 243267.8 283492.8 331588.7 401401.6 480683.5 549897.9 #VALUE! 80577.5 144066.6 203540.6 253691.5 291052.6 339059 408227.1 484176.3 561579.8 87307.82 129574.4 184170.1 229190.1 279532.4 360882.9 427801.6 489538.7 542335.7 89439.86 152006.8 215931.6 268893.6 293191.2 361373.2 404019.7 458550.3

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15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

#VALUE! 5823.962 10290.73 13428.08 17656.26 19432.81 21985.11 23896.86 30556.46 34846.16 #VALUE! 4774.094 9836.557 11886.51 16036.11 18687.72 21858.18 26460.23 31686.46 36249.04 #VALUE! 5311.635 9496.808 13417.31 16723.24 19186.06 22350.63 26910.16 31916.7 37019.1 5755.295 8541.493 12140.41 15108.11 18426.66 23789.25 28200.5 32270.18 35750.54 5895.838 10020.23 14234.12 17725.35 19327.04 23821.57 26632.81 30227.45

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Vel 0.758229 1.339763 1.748217 2.298689 2.52998 2.862267 3.11116 3.978182 4.536663 Vel 0.62 1.28 1.55 2.09 2.43 2.85 3.44 4.13 4.72 Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561 0.75 1.11 1.58 1.97 2.40 3.10 3.67 4.20 4.65 0.77 1.30 1.85 2.31 2.52 3.10 3.47 3.94

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3952.363 998.3795 1857.162 2161.295 2441.875 2624.52 2861.127 3247.374 3540.343 4056.825 889.0085 1521.774 2126.644 2730.868 3121.689 3522.993 4152.754 922.0801 1565.064 1679.369 2249.668 2227.969 2716.355 3066.233 3597.444 4107.391 1048.957 1534.846 1779.974 2223.705 2342.924 2874.383 3095.506 3686.68 3988.522 914.2035 1454.451 1555.335 2199.68 2436.893 2900.474 2917.17 3607.21 3976.339 1004.491 1568.337 1752.876

SC

292.6269 73.91849 137.5014 160.0189 180.7927 194.3154 211.8334 240.4306 262.1216 300.3611 65.82082 112.6698 157.4535 202.1893 231.1251 260.837 307.4635 68.26939 115.875 124.3379 166.562 164.9554 201.1147 227.0192 266.3492 304.1049 77.66317 113.6377 131.7865 164.6397 173.4665 212.8149 229.1865 272.9561 295.304 67.68622 107.6853 115.1546 162.8609 180.4238 214.7467 215.9827 267.0723 294.402 74.371 116.1173 129.7803

M AN U

526290.7 94248.47 204746.7 247484.1 288276.4 315476.6 351419.7 411689.8 458628.9 543735.4 81524.3 159621.8 242534.4 331535.9 391869.9 455821.2 559854.2 85332.71 165317.9 180545.8 260197.3 257064 329335 383187.4 467893.8 552220.2 100254 161337.7 194165.4 256449.1 273749 353456.2 387765.5 482446.4 532316.2 84422.53 150844.2 164034.4 252990.5 287541.3 357471.2 360045 469482.1 530284.5 94970.23 165750.2 190477.5

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15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

34692.86 6212.82 13496.81 16314.04 19003.06 20796.08 23165.44 27138.42 30232.63 35842.8 5374.048 10522.2 15987.76 21854.71 25831.9 30047.54 36905.35 5625.096 10897.69 11901.5 17152.1 16945.55 21709.62 25259.55 30843.37 36402.12 6608.704 10635.31 12799.3 16905.02 18045.42 23299.68 25561.34 31802.66 35090.06 5565.097 9943.588 10813.08 16677.03 18954.6 23564.35 23734.02 30948.06 34956.13 6260.398 10926.18 12556.2

AC C

4.52 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418 0.70 1.37 2.08 2.85 3.36 3.91 4.80

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2257.352 2365.024 2768.268 2927.392 3553.058 3961.52 803.2339 1420.566 1499.242 1965.644 2151.631 2579.476 2883.869 3438.884 3743.633 902.7711 1428.844 1703.752 2108.964 2296.182 2705.142 3015.379 3662.634 3992.714 885.5582 1219.384 1485.108 1828.159 2069.969 2588.067 2903.419 3362.635 3600.096 937.577 1421.87 1731.072 2127.646 2306.481 2735.096 2961.279 3457.199 3769.163 898.955 1552.341 1696.466 2012.643 2106.711

M AN U

167.1308 175.1027 204.9583 216.7396 263.0629 293.3049 59.4702 105.1765 111.0015 145.5332 159.3034 190.9804 213.5173 254.6097 277.1729 66.83978 105.7894 126.1432 156.1444 170.0058 200.2846 223.254 271.1758 295.6144 65.56537 90.28131 109.9551 135.3541 153.2573 191.6165 214.9647 248.9643 266.5456 69.41676 105.2731 128.1659 157.5277 170.7683 202.5023 219.2485 255.9657 279.063 66.55724 114.9329 125.6037 149.013 155.9776

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261308.6 276980.4 337221.2 361622.8 460688.7 527815.4 71813.69 146464.2 156673 219804.1 246101.6 308723.1 354914.9 442259 491780.6 83104.93 147531.8 183828.5 240016.5 266939.4 327636.5 375259.8 478516.1 533015.7 81129 121012.5 154829 200757.6 234482 310008.9 357924.9 430035.5 468325 87129.13 146632.3 187520.5 242677.2 268436.8 332177.6 366862.9 445205.2 495976.2 82666.04 163639.6 182846.3 226393.1 239696.1

EP

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

AC C

17225.35 18258.43 22229.48 23838.02 30368.41 34793.37 4733.928 9654.858 10327.82 14489.39 16222.91 20350.89 23395.84 29153.53 32417.97 5478.242 9725.234 12117.9 15821.79 17596.53 21597.66 24736.97 31543.58 35136.17 5347.989 7977.094 10206.26 13233.86 15456.95 20435.66 23594.26 28347.76 30871.78 5743.516 9665.941 12361.27 15997.18 17695.24 21897.01 24183.45 29347.74 32694.54 5449.311 10787.06 12053.15 14923.74 15800.66

RI PT

ACCEPTED MANUSCRIPT

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

286166.1 327696.2 388219.8 452039.2 74314.91 142951.1 197652.6 268687.9 310975.8 374645.1 448248.3

179.7332 200.3137 229.4012 259.1042 61.12155 103.1534 133.6767 170.8961 192.0945 222.9614 257.3645

2427.565 2705.536 3098.406 3499.589 825.5378 1393.241 1805.503 2308.206 2594.523 3011.427 3476.091

AC C

EP

TE D

M AN U

SC

18863.95 21601.59 25591.28 29798.23 4898.807 9423.274 13029.18 17711.79 20499.4 24696.45 29548.34

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

Re

RePR 15.9 14473.49 15.9 76391.51

RI PT

M AN U TE D EP AC C

Pr 5000 40000

SC

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04601731 73.228819 60.5341941 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8333743 114.02112 103.854921 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6091968 145.27525 136.771494 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5438912 184.39553 180.878658 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9080838 216.74782 216.986307 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1383667 241.10514 246.006532 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2960579 247.95851 253.655111 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575419 277.97486 290.119402 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7894632 294.97439 309.411637 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718015 4523.427 42245.56 5.5 15.9 671704.4 0.105

0 550000

0 40000

0 5

1 1

ACCEPTED MANUSCRIPT

RI PT

1.14

Mo

1.12 1.1

SC

1.08

M AN U

1.06 1.04 1.02 1

0.2

AC C

EP

TE D

0

13 nm 50 nm

0.4 Φ%

0.6

ACCEPTED MANUSCRIPT

0.05vf50nm 0.1vf50nm 0.2vf50nm 0.3vf50nm 0.5vf50nm 1.412 1.427 1.443 1.46 1.49 1.31 1.319 1.335 1.351 1.385 1.117 1.125 1.14 1.157 1.19 0.953 0.96 0.976 0.993 1.027 0.818 0.826 0.842 0.86 0.897 0.763 0.77 0.788 0.806 0.845

mu_13nm mu_50nm 1.395 1.395 1.418 1.41 1.44 1.414 1.457 1.433 1.47 1.45 1.54 1.505

K_13 0.100667 0.108167 0.11 0.112833 0.114667 0.123

SC

RI PT

0 0.05 0.1 0.2 0.3 0.5

M AN U TE D EP

0.05vf13nm 0.1vf13nm 0.2vf13nm 0.3vf13nm 0.5vf13nm 1.422 1.433 1.456 1.477 1.524 1.314 1.324 1.346 1.369 1.415 1.12 1.131 1.152 1.174 1.22 0.955 0.966 0.987 1.009 1.057 0.82 0.831 0.854 0.878 0.93 0.764 0.776 0.8 0.825 0.88

AC C

Volume Fraction 0 0.05 0.1 0.2 0.3 0.5

K_50 Rho 0.100667 809 0.106 810.5905 0.107167 812.181 0.1095 815.362 0.111833 818.543 0.117833 824.905

Cp 2093 2089.732 2086.477 2080.005 2073.584 2060.889

Mo_13_dittus-Boelter Mo_50_Dittus-Boelter 485.5077829 485.5077829 1.04516425 1.031090693 1.056706651 1.038392054 1.070391864 1.04910073 1.078288737 1.060363827 1.115216623 1.08360869

ACCEPTED MANUSCRIPT

7000 0.05% 13nm 6000

RI PT

0.05% 50nm 0.2% 13nm 0.2% 50nm

SC

4000

M AN U

3000

2000

0

10000

EP

0

TE D

1000

AC C

h (w/m2k)

5000

20000

0.3% 13nm 0.3% 50nm 0.5% 13nm 0.5% 50nm Pure Kerosene

30000

Re

40000

50000

60000

ACCEPTED MANUSCRIPT

Nu_DB 65.30587 111.9013 130.5425 175.1432 172.3848 201.7167 234.2418 264.4811 297.8724

Nu_Gen 52.65631 101.9563 121.436 171.1343 168.0321 201.7188 238.1897 274.8055 314.1761

(Hnf/Hpf)V 1.10476451 1.07797523 1.01117157 1.0026325 1.0162503 1.05518168 1.04139384 1.07324153 1.08373015

M AN U TE D EP

(Hnf/Hpf)Re 1.075865026 1.076560447 1.082089197 1.065081018 1.079320978 1.090168255 1.127583933 1.08016342 1.087367899

RI PT

h_exp-0.05sK Nu_exp-0.05s 996.5051 0.117904 65.07888109 1682.359 0.117007 110.7126768 1891.455 0.114796 126.870515 2509.066 0.115016 167.9756577 2502.653 0.115023 167.5351509 3007.808 0.115881 199.861825 3511.754 0.114451 236.2631742 3969.847 0.116747 261.8304753 4510.361 0.116847 297.2255786

SC

Vel Pr Re^0.8 Pr^0.4 Pe 0.698716 13.9586495 13807.9887 77437.65 1.386518 14.5095547 24215.8436 154778.6 1.73881 16.1181284 30089.3486 197782.3 2.501792 15.937742 40097.8984 283984.9 2.4521 15.9363724 39464.3398 278393.2 2.944027 15.2837703 45035.2234 331804.9 3.632241 16.4055232 54567.068 414396.2 4.077402 14.6907251 57662.4105 456410 4.72499 14.6135602 64737.5239 528148.6

AC C

RE 5547.646 10667.36 12270.8 17818.39 17469.05 21709.62 25259.55 31067.9 36140.99

(Hnf/Hpf)Pe 1.16385706 1.129098234 1.043345026 1.036233883 1.050160357 1.096795616 1.071947184 1.121686405 1.133935255

0.05% 13nm0.05% 13nm0.05% 13nm 1.083228 1.054891 1.141168 1.030881 1.029528 1.079771 0.979 1.047661 1.01015 0.998521 1.060714 1.031985 0.992135 1.053709 1.02524 1.015733 1.049411 1.055791 1.017159 1.101343 1.047001 1.0871 1.094111 1.136171 1.091849 1.095514 1.14243

ACCEPTED MANUSCRIPT

K 0.111858 0.112378 0.110702 0.111413 0.1102 0.111389 0.111076 0.112173 0.111341

Nu_exp-0.5lNu_DB 75.93648 74.21862 112.1558 109.9809 140.3751 138.304 168.7731 166.8019 185.5256 186.3786 224.8539 215.7783 246.1604 233.3266 276.9776 269.4173 316.0861 296.4203

Nu_Gen 61.61831 100.0557 129.9734 162.225 183.2382 217.8415 237.7497 280.8886 311.7457

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe0.05% 50nm0.05% 50nm0.05% 50nm 1.099152 1.099152 1.11 1.05866 1.05866 1.069107784 1.113433 1.113433 1.128392 1.050546 1.050546 1.064659623 1.048862 1.048862 1.050909 1.013903 1.013903 1.015881482 1.071331 1.071331 1.078583 1.042452 1.042452 1.04950811 1.010491 1.010491 1.008793 1.001131 1.001131 0.999448778 1.102514 1.102514 1.109732 1.09573 1.09573 1.102903575 1.104432 1.104432 1.109397 1.126202 1.126202 1.131265382 1.115429 1.115429 1.128802 1.059624 1.059624 1.072328062 1.126469 1.126469 1.133281 1.095379 1.095379 1.102003867

RI PT

h_exp-05l 1103.125 1636.863 2018.149 2442.011 2655.192 3252.765 3550.96 4034.975 4570.553

M AN U

SC

Re^0.8 Pr^0.4 Pe 16196.9517 93294.23935 23464.2506 149681.3739 31871.4236 212550.6416 37151.5957 261122.9317 44053.3846 315206.0235 48115.4826 360595.7866 52801.0675 402532.3488 57990.7295 462121.5199 66256.6455 537361.1463

TE D

Pr 14.71455 14.16976 16.1123 15.22325 16.80809 15.25252 15.63185 14.3803 15.31377

EP

Vel 0.798449 1.286689 1.801282 2.22622 2.659148 3.073434 3.422132 3.9654 4.577204

AC C

RE 6340.269 10563.44 13191.82 17152.91 18753.23 23641.72 25750.78 32135.73 35090.06

ACCEPTED MANUSCRIPT

Nu_exp-0.2sNu_DB 61.4864 56.11831 101.3997 99.65 117.0625 113.4808 144.1866 145.8541 165.7678 163.2296 190.284 187.2735 221.3851 216.3877 265.5391 251.2614 288.2756 278.3376

Nu_Gen 43.53593 89.28494 103.3352 139.4522 158.355 186.1855 218.9646 259.7459 291.0525

(Hnf/Hpf)V 1.275443102 1.170830127 1.122631027 1.106681242 1.109358997 1.144029489 1.127668695 1.180545902 1.141684605

(Hnf/Hpf)Re 1.284093219 1.194488999 1.227873383 1.167623135 1.207360834 1.198318539 1.213244673 1.248157954 1.227576581

RI PT

h_exp-0.2s K 1047.632 0.131196 1714.759 0.130214 1913.001 0.125831 2396.274 0.127968 2714.888 0.126108 3173.68 0.128426 3644.946 0.126775 4407.746 0.127814 4746.987 0.126795

M AN U

SC

Re^0.8 Pr^0.4 Pe 11433.4124 62118.39 20582.3174 128792.6 25193.9201 160907.9 31208.9145 213539.6 36054.3463 252393.2 39768.2765 290018.6 47238.9297 355530.6 53855.0394 422040.8 60702.7119 486622

TE D

Pr 13.12195 13.42481 15.1415 14.239 15.01334 14.05985 14.72286 14.27954 14.69851

EP

Vel 0.621545 1.280633 1.547519 2.087761 2.432977 2.845743 3.444888 4.125298 4.719306

AC C

RE 4733.928 9593.626 10626.95 14996.81 16811.26 20627.44 24148.21 29555.64 33106.89

(Hnf/Hpf)Pe0.2% 13nm0.2% 13nm0.2% 13nm 1.459534 1.201224 1.20937 1.374602 1.333129 1.070038 1.09166 1.218366 1.244615 1.003994 1.098114 1.113087 1.243185 0.99789 1.052841 1.120974 1.232173 0.999596 1.087901 1.110258 1.288856 1.030742 1.079656 1.161228 1.257683 1.033747 1.112196 1.152933 1.325912 1.10662 1.169998 1.242883 1.274226 1.039619 1.117833 1.160312

ACCEPTED MANUSCRIPT

K 0.125829 0.125479 0.121532 0.123265 0.122087 0.123829 0.122335 0.124765 0.123391

Nu_exp-0.2lNu_DB 66.72749 62.98494 111.4692 100.0137 138.1021 128.3917 167.2666 155.0902 186.1079 171.6368 216.0257 196.3328 243.429 224.3843 286.1464 262.6416 310.7312 293.1144

Nu_Gen 50.56447 89.71656 119.5899 149.7068 167.8881 196.5216 228.0024 273.6766 308.9321

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.218923 1.195139 1.348647044 1.27567 1.25802 1.410155626 1.161001 1.237999 1.252011073 1.195828 1.22944 1.303905023 1.180646 1.243792 1.277970146 1.230182 1.250703 1.346278479 1.180497 1.248452 1.279710732 1.234643 1.233206 1.359003846 1.177607 1.207667 1.285088932

RI PT

h_exp-0.2l 1090.419 1816.499 2179.715 2677.686 2950.823 3474.048 3867.521 4636.501 4979.387

SC

Re^0.8 Pr^0.4 Pe 12902.1264 72085.25 20590.1435 129029.1 28553.2441 188025.5 33282.4345 231137 37719.4422 267611.9 41666.9541 307506 49399.4289 374652.4 54765.8073 435952.8 62745.437 511129.2

M AN U

13.241 13.352 15.18486 14.30861 14.8869 14.04574 14.93123 13.63922 14.24912

TE D

Pr

EP

Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561

AC C

RE 5444.095 9663.65 12382.43 16153.7 17976.33 21893.18 25091.86 31963.17 35870.93

0.2% 50nm0.2% 50nm0.2% 50nm 1.176226 1.153275 1.301406 1.193207 1.176698 1.318999 1.072299 1.143413 1.156355 1.109216 1.140394 1.209465 1.072065 1.129403 1.160439 1.117188 1.135824 1.222621 1.099887 1.163201 1.192325 1.151444 1.150105 1.267425 1.096179 1.12416 1.196228

ACCEPTED MANUSCRIPT

Nu_exp-0.3sNu_DB 67.6355 64.03218 102.797 88.42092 126.7817 114.3404 156.1554 137.6449 174.9715 159.5505 222.3501 196.6073 248.0932 223.3202 286.7741 251.8322 314.4038 271.8178

Nu_Gen 51.22818 77.12423 104.0727 130.0495 153.8867 195.9333 226.02 259.8369 282.7461

(Hnf/Hpf)V 1.185641083 1.329027593 1.195267188 1.252527278 1.180590009 1.229592283 1.185193237 1.248724405 1.252069608

M AN U TE D

(Hnf/Hpf)Re 1.254279776 1.374293179 1.332620188 1.353085775 1.31848137 1.355397074 1.340037919 1.359803446 1.388479936

RI PT

h_exp-0.3s K 1130.946 0.128753 1738.584 0.130228 2071.507 0.125812 2585.771 0.127504 2856.874 0.125723 3650.063 0.126402 4031.153 0.125114 4730.886 0.127026 5148.601 0.126093

SC

Pr Re^0.8 Pr^0.4 Pe 14.21163 13685.3757 76235.97 13.65727 18452.0874 111870.6 15.51732 25760.9561 164436.5 14.7233 30049.3645 201972.8 15.55859 36004.1494 249717 15.22936 43800.6874 320760.4 15.87839 51013.3747 384063.8 14.90663 55387.4257 432433.3 15.38466 60926.0106 483316.3

EP

Vel 0.749289 1.112027 1.580575 1.966943 2.398989 3.09715 3.671456 4.201294 4.654405

AC C

RE 5364.338 8191.285 10596.97 13717.9 16050.11 21061.97 24187.83 29009.45 31415.48

(Hnf/Hpf)Pe 1.337506581 1.51288134 1.324554106 1.402612492 1.307718957 1.367532613 1.307640674 1.395690271 1.389587622

0.3% 13nm 0.3% 13nm 0.3% 13nm 1.048587 1.109291 1.182897 1.16447 1.204131 1.32556 1.050256 1.170945 1.163857 1.086559 1.173792 1.216757 1.031577 1.152064 1.14266 1.079922 1.190414 1.201072 1.029352 1.163836 1.135699 1.089969 1.186926 1.218251 1.123628 1.246045 1.247039

ACCEPTED MANUSCRIPT

K 0.102582 0.126427 0.123222 0.124255 0.124042 0.124885 0.124227 0.126915 0.125735

Nu_exp-0.3lNu_DB 85.99118 67.21606 120.1099 102.416 150.6336 132.1555 188.1594 158.9348 188.3668 170.0043 239.7737 202.3768 255.5954 220.067 284.4845 248.5357 312.3335 275.2068

Nu_Gen 54.71687 92.06135 123.5585 153.6267 165.9727 203.0339 223.0541 257.2314 287.9402

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.178051 1.195691 1.306495845 1.32676 1.351873 1.474992721 1.224673 1.340405 1.334858122 1.294313 1.382152 1.420067544 1.207024 1.295278 1.322774477 1.308613 1.377506 1.441560308 1.269144 1.356096 1.392390322 1.304148 1.315634 1.454974513 1.270445 1.312958 1.406691714

RI PT

h_exp-0.3l 1145.606 1972.101 2410.568 3036.336 3034.471 3888.86 4123.626 4689.025 5100.145

M AN U

SC

Re^0.8 Pr^0.4 Pe 14105.5796 79778.58 21516.0126 135176.6 29731.7483 196826.1 34929.1963 243096.3 37532.066 265444.5 43867.2776 325060.5 48387.8929 365279.5 51687.2146 405986.3 58611.4662 470388.7

TE D

Pr 13.78509 13.8103 15.48003 14.88776 15.0009 14.54944 14.89987 13.57908 14.12815

EP

Vel 0.767586 1.304545 1.853157 2.307685 2.51621 3.101358 3.467357 3.935347 4.516705

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

0.3% 50nm0.3% 50nm0.3% 50nm 1.07283 1.088895 1.189802 1.197519 1.220186 1.331312 1.092166 1.195376 1.190429 1.155977 1.234428 1.268291 1.071911 1.150286 1.174704 1.167418 1.228876 1.28602 1.112423 1.188638 1.22045 1.157526 1.167722 1.291397 1.108565 1.145661 1.227452

ACCEPTED MANUSCRIPT

Nu_Gen 52.01392 109.5255 126.9408 149.2917 161.4681 182.3632 209.2581 236.2014 272.1572

(Hnf/Hpf)V 1.370130052 1.296301535 1.283756653 1.324405837 1.289846457 1.346430765 1.318479734 1.353072011 1.340044821

(Hnf/Hpf)Re 1.537441677 1.513339277 1.592212691 1.582594713 1.55742004 1.551848589 1.543975997 1.500626002 1.532098163

(Hnf/Hpf)Pe0.5% 13nm 1.599731 1.489318 1.447077 1.5095 1.465359 1.554578 1.51327 1.589468 1.552256

RI PT

Nu_exp-0.5sNu_DB 79.47883 64.97121 142.8185 119.4484 168.6683 136.156 193.8406 155.8581 203.7651 166.9166 227.138 184.7466 254.3888 208.6477 276.3672 231.0418 319.2169 262.5832

SC

h_exp-0.5s K 1389.448 0.134611 2445.348 0.13184 2818.264 0.128659 3284.955 0.130489 3438.53 0.129937 3912.965 0.13265 4349.012 0.131639 4865.766 0.135567 5521.925 0.133197

M AN U

Re^0.8 Pr^0.4 Pe 14144.63 78838.83 27114.33 174758.2 32807.68 216325.8 36219.19 248522.8 39187.97 273075.1 41381.97 298100.7 47507.67 351834.9 49632.14 380732.8 58319.86 459362

TE D

Pr 14.65539 15.71246 17.3558 16.33912 16.62016 15.36753 15.79295 14.33289 15.15173

EP

Vel 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418

AC C

RE 5379.509 11122.27 12464.18 15210.3 16430.35 19398.08 22277.97 26563.57 30317.47

1.058302489 1.099738065 1.108348345 1.135471921 1.101384653 1.176735755 1.143075549 1.138414644 1.156510411

0.5% 13nm0.5% 13nm 1.187536 1.235649 1.283865 1.263487 1.374658 1.249353 1.356829 1.294162 1.329863 1.251252 1.356264 1.358649 1.338573 1.311951 1.26256 1.337308 1.32226 1.339657

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

RE Vel Pr Re^0.8 Pr^0.4 Pe h_exp-0.5l K Nu_exp-0.5lNu_DB Nu_Gen (Hnf/Hpf)V (Hnf/Hpf)Re (Hnf/Hpf)Pe0.5% 50nm 4922.87805 0.699653673 14.59087644 13117.66821 71829.10536 1284.608568 0.128112 77.2099 60.41373 47.33686322 1.422590845 1.525969862 1.593409 9750.402834 1.369898174 14.33141543 22259.076 139737.0737 2046.873625 0.128373 122.7747 103.6243 93.08967541 1.324207643 1.407418926 1.490866 13180.32319 2.081466016 16.62645037 32865.51092 219141.9895 2971.416699 0.124479 183.8058 139.955 131.5091157 1.375573466 1.605362507 1.51001 18148.94292 2.845290758 16.48304217 42084.13815 299149.7916 3849.468936 0.124687 237.7217 180.1457 176.4150658 1.387762624 1.610164159 1.525059 20828.32383 3.363085294 17.08011992 48687.1522 355750.2688 4210.704877 0.123891 261.7002 204.0082 203.0491413 1.327945304 1.577544977 1.45223 24946.99404 3.911925305 16.48847461 54299.40348 411337.8779 5065.259953 0.124683 312.8139 232.3885 235.9882169 1.415484068 1.64262173 1.555391 29650.52862 4.804751989 17.15686942 64873.00241 508710.2476 5982.985833 0.123804 372.1111 271.0997 280.3462331 1.418393995 1.689827704 1.550024

0.5% 50nm 1.120787317 1.123796049 1.18396894 1.210760282 1.123654624 1.237425533 1.230750039

1.202234411 1.194413758 1.381750515 1.404795588 1.334855963 1.43599078 1.466274899

0.5% 50nm 1.255366 1.265231 1.29968 1.330545 1.228819 1.359733 1.344966

ACCEPTED MANUSCRIPT

Re

RePR 15.9 14473.49 15.9 76391.51

RI PT

M AN U TE D EP AC C

Pr 5000 40000

SC

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04602 73.22882 60.53419 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8334 114.0211 103.8549 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6092 145.2753 136.7715 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5439 184.3955 180.8787 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9081 216.7478 216.9863 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1384 241.1051 246.0065 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2961 247.9585 253.6551 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575 277.9749 290.1194 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7895 294.9744 309.4116 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718 4523.427 42245.56 5.5 15.9 671704.4 0.105

0 550000

0 40000

0 5

1 1

ACCEPTED MANUSCRIPT

5000 4500

RI PT

4000

3000

SC

2500 2000 1500 1000

M AN U

h (w/m2k)

3500

Kerosene+ 0.3% Alumina (Current Study)

500

ATF+0.3% Al2O3 (Sonawane et al 2012) 10000

AC C

EP

TE D

0 5000

15000

Re

20000

25000

ACCEPTED MANUSCRIPT h_Sonawane et al 2012 1850 2200 2700 3100 3500 4050

RI PT

8500 11500 13500 16500 19000 22500

EP

TE D

M AN U

SC

h_exp-0.3l Re 1145.60574 1972.100971 2410.567547 3036.336297 3034.470661 3888.860273 4123.626389 4689.025266 5100.145397

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

ACCEPTED MANUSCRIPT

7000 0.05% 13nm 6000

RI PT

0.05% 50nm 0.2% 13nm 0.2% 50nm

SC

4000

M AN U

3000

2000

0

2

EP

0

TE D

1000

AC C

h (w/m2k)

5000

0.3% 13nm 0.3% 50nm 0.5% 13nm 0.5% 50nm Pure Kerosene

4

u (m/s)

6

8

ACCEPTED MANUSCRIPT

0.80 1.29 1.80 2.23 2.66 3.07 3.42 3.97 4.58 Vel 0.70 1.26 1.56 2.31 2.75 3.18 3.28 4.03 4.73

H 329.594 679.478 1183.04 1636.336 2059.792 2462.359 2849.026 3222.952 3586.306 3940.664 4287.216 4626.894 4960.442 5288.47 5611.485 5929.914 6244.122 888.0548 1536.526 1841.624 2463.771 2424.544 2806.421 3320.008 3641.717 4097.511 #VALUE! 888.0548 1447.366 1894.37 2244.16 2586.982 2904.682 3165.46 3561.468 3994.658 #VALUE! 891.291 1425.054 1690.124 2312.586 2655.211 2981.576 3059.105 3605.963 4104.4

RI PT

Nu 24.17023 50.30751 87.59046 121.1518 152.5038 182.3093 210.9375 238.6224 265.5246 291.7607 317.4189 342.5681 367.2635 391.5502 415.4657 439.0417 462.3052 65.75021 113.762 136.351 182.4138 179.5095 207.7831 245.8083 269.6272 303.3734 #VALUE! 65.75021 107.1607 140.2562 166.1542 191.5361 215.0582 234.3658 263.6856 295.7584 #VALUE! 65.98982 105.5088 125.1342 171.2203 196.5877 220.7513 226.4915 266.9799 303.8835

SC

Pe 23304.19 58260.47 116520.9 174781.4 233041.9 291302.3 349562.8 407823.3 466083.8 524344.2 582604.7 640865.2 699125.6 757386.1 815646.6 873907 932167.5 81415 161558.4 202607.8 291511.2 285721 343040.8 423232.1 475102.7 550560.2 #VALUE! 81415 149926.2 209887.1 259401.3 309846.4 358119.5 398750 462052.1 533340.2 #VALUE! 81786.03 147042.8 181992.3 269325.2 320094.7 370008.8 382074.3 469279.1 551717.6

M AN U

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

TE D

Vel

Re Pr 1536.202 3840.506 7681.011 11521.52 15362.02 19202.53 23043.03 26883.54 30724.04 34564.55 38405.06 42245.56 46086.07 49926.57 53767.08 57607.58 61448.09 5366.843 10649.86 13355.82 19216.29 18834.61 22613.1 27899.28 31318.57 36292.7 #VALUE! 5366.843 9883.071 13835.67 17099.62 20424.94 23607.08 26285.43 30458.28 35157.56 #VALUE! 5391.301 9692.999 11996.86 17753.8 21100.51 24390.82 25186.17 30934.68 36368.99

EP

0.20 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 0.70 1.39 1.74 2.50 2.45 2.94 3.63 4.08 4.72

AC C

V

#VALUE! 948.068 1494.933 1849.591 2302.415 2485.954 2743.895 2933.17 3570.648 3966.328 #VALUE! 808.6815 1441.913 1677.676 2131.788 2409.405 2731.215 3182.288 3675.899 4093.567 #VALUE! 880.739 1401.932 1848.404 2204.555 2460.67 2780.331 3225.505 3697.252 4162.99 939.1149 1287.928 1706.285 2032.511 2382.44 2922.599 3348.653 3729.974 4048.468 957.4169 1463.412 1937.89 2309.62 2475.124 2925.775 3198.882 3539.858

SC

#VALUE! 70.1935 110.6826 136.9409 170.4673 184.0562 203.1538 217.1674 264.3653 293.6608 #VALUE! 59.87353 106.7571 124.2126 157.8343 178.3886 202.215 235.6117 272.1579 303.0814 #VALUE! 65.20856 103.7969 136.853 163.2219 182.1842 205.8514 238.8114 273.7388 308.2214 69.53063 95.35623 126.3307 150.484 176.3922 216.3847 247.9291 276.1615 299.7424 70.88568 108.3488 143.4784 171.0007 183.2544 216.6199 236.8403 262.0856

M AN U

#VALUE! 88349.5 156110.4 203703.9 267845.4 294795.7 333514.1 362515.3 463541.5 528616.3 #VALUE! 72423.01 149220.6 180318.3 243267.8 283492.8 331588.7 401401.6 480683.5 549897.9 #VALUE! 80577.5 144066.6 203540.6 253691.5 291052.6 339059 408227.1 484176.3 561579.8 87307.82 129574.4 184170.1 229190.1 279532.4 360882.9 427801.6 489538.7 542335.7 89439.86 152006.8 215931.6 268893.6 293191.2 361373.2 404019.7 458550.3

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

#VALUE! 5823.962 10290.73 13428.08 17656.26 19432.81 21985.11 23896.86 30556.46 34846.16 #VALUE! 4774.094 9836.557 11886.51 16036.11 18687.72 21858.18 26460.23 31686.46 36249.04 #VALUE! 5311.635 9496.808 13417.31 16723.24 19186.06 22350.63 26910.16 31916.7 37019.1 5755.295 8541.493 12140.41 15108.11 18426.66 23789.25 28200.5 32270.18 35750.54 5895.838 10020.23 14234.12 17725.35 19327.04 23821.57 26632.81 30227.45

AC C

Vel 0.758229 1.339763 1.748217 2.298689 2.52998 2.862267 3.11116 3.978182 4.536663 Vel 0.62 1.28 1.55 2.09 2.43 2.85 3.44 4.13 4.72 Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561 0.75 1.11 1.58 1.97 2.40 3.10 3.67 4.20 4.65 0.77 1.30 1.85 2.31 2.52 3.10 3.47 3.94

RI PT

ACCEPTED MANUSCRIPT

3952.363 998.3795 1857.162 2161.295 2441.875 2624.52 2861.127 3247.374 3540.343 4056.825 889.0085 1521.774 2126.644 2730.868 3121.689 3522.993 4152.754 922.0801 1565.064 1679.369 2249.668 2227.969 2716.355 3066.233 3597.444 4107.391 1048.957 1534.846 1779.974 2223.705 2342.924 2874.383 3095.506 3686.68 3988.522 914.2035 1454.451 1555.335 2199.68 2436.893 2900.474 2917.17 3607.21 3976.339 1004.491 1568.337 1752.876

SC

292.6269 73.91849 137.5014 160.0189 180.7927 194.3154 211.8334 240.4306 262.1216 300.3611 65.82082 112.6698 157.4535 202.1893 231.1251 260.837 307.4635 68.26939 115.875 124.3379 166.562 164.9554 201.1147 227.0192 266.3492 304.1049 77.66317 113.6377 131.7865 164.6397 173.4665 212.8149 229.1865 272.9561 295.304 67.68622 107.6853 115.1546 162.8609 180.4238 214.7467 215.9827 267.0723 294.402 74.371 116.1173 129.7803

M AN U

526290.7 94248.47 204746.7 247484.1 288276.4 315476.6 351419.7 411689.8 458628.9 543735.4 81524.3 159621.8 242534.4 331535.9 391869.9 455821.2 559854.2 85332.71 165317.9 180545.8 260197.3 257064 329335 383187.4 467893.8 552220.2 100254 161337.7 194165.4 256449.1 273749 353456.2 387765.5 482446.4 532316.2 84422.53 150844.2 164034.4 252990.5 287541.3 357471.2 360045 469482.1 530284.5 94970.23 165750.2 190477.5

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

34692.86 6212.82 13496.81 16314.04 19003.06 20796.08 23165.44 27138.42 30232.63 35842.8 5374.048 10522.2 15987.76 21854.71 25831.9 30047.54 36905.35 5625.096 10897.69 11901.5 17152.1 16945.55 21709.62 25259.55 30843.37 36402.12 6608.704 10635.31 12799.3 16905.02 18045.42 23299.68 25561.34 31802.66 35090.06 5565.097 9943.588 10813.08 16677.03 18954.6 23564.35 23734.02 30948.06 34956.13 6260.398 10926.18 12556.2

AC C

4.52 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418 0.70 1.37 2.08 2.85 3.36 3.91 4.80

RI PT

ACCEPTED MANUSCRIPT

SC

2257.352 2365.024 2768.268 2927.392 3553.058 3961.52 803.2339 1420.566 1499.242 1965.644 2151.631 2579.476 2883.869 3438.884 3743.633 902.7711 1428.844 1703.752 2108.964 2296.182 2705.142 3015.379 3662.634 3992.714 885.5582 1219.384 1485.108 1828.159 2069.969 2588.067 2903.419 3362.635 3600.096 937.577 1421.87 1731.072 2127.646 2306.481 2735.096 2961.279 3457.199 3769.163 898.955 1552.341 1696.466 2012.643 2106.711

M AN U

167.1308 175.1027 204.9583 216.7396 263.0629 293.3049 59.4702 105.1765 111.0015 145.5332 159.3034 190.9804 213.5173 254.6097 277.1729 66.83978 105.7894 126.1432 156.1444 170.0058 200.2846 223.254 271.1758 295.6144 65.56537 90.28131 109.9551 135.3541 153.2573 191.6165 214.9647 248.9643 266.5456 69.41676 105.2731 128.1659 157.5277 170.7683 202.5023 219.2485 255.9657 279.063 66.55724 114.9329 125.6037 149.013 155.9776

TE D

261308.6 276980.4 337221.2 361622.8 460688.7 527815.4 71813.69 146464.2 156673 219804.1 246101.6 308723.1 354914.9 442259 491780.6 83104.93 147531.8 183828.5 240016.5 266939.4 327636.5 375259.8 478516.1 533015.7 81129 121012.5 154829 200757.6 234482 310008.9 357924.9 430035.5 468325 87129.13 146632.3 187520.5 242677.2 268436.8 332177.6 366862.9 445205.2 495976.2 82666.04 163639.6 182846.3 226393.1 239696.1

EP

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

AC C

17225.35 18258.43 22229.48 23838.02 30368.41 34793.37 4733.928 9654.858 10327.82 14489.39 16222.91 20350.89 23395.84 29153.53 32417.97 5478.242 9725.234 12117.9 15821.79 17596.53 21597.66 24736.97 31543.58 35136.17 5347.989 7977.094 10206.26 13233.86 15456.95 20435.66 23594.26 28347.76 30871.78 5743.516 9665.941 12361.27 15997.18 17695.24 21897.01 24183.45 29347.74 32694.54 5449.311 10787.06 12053.15 14923.74 15800.66

RI PT

ACCEPTED MANUSCRIPT

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

286166.1 327696.2 388219.8 452039.2 74314.91 142951.1 197652.6 268687.9 310975.8 374645.1 448248.3

179.7332 200.3137 229.4012 259.1042 61.12155 103.1534 133.6767 170.8961 192.0945 222.9614 257.3645

2427.565 2705.536 3098.406 3499.589 825.5378 1393.241 1805.503 2308.206 2594.523 3011.427 3476.091

AC C

EP

TE D

M AN U

SC

18863.95 21601.59 25591.28 29798.23 4898.807 9423.274 13029.18 17711.79 20499.4 24696.45 29548.34

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

Re

RePR 15.9 14473.49 15.9 76391.51

RI PT

M AN U TE D EP AC C

Pr 5000 40000

SC

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04601731 73.228819 60.5341941 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8333743 114.02112 103.854921 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6091968 145.27525 136.771494 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5438912 184.39553 180.878658 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9080838 216.74782 216.986307 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1383667 241.10514 246.006532 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2960579 247.95851 253.655111 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575419 277.97486 290.119402 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7894632 294.97439 309.411637 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718015 4523.427 42245.56 5.5 15.9 671704.4 0.105

0 550000

0 40000

0 5

1 1

ACCEPTED MANUSCRIPT

Nu_DB 65.30587 111.9013 130.5425 175.1432 172.3848 201.7167 234.2418 264.4811 297.8724

Nu_Gen 52.65631 101.9563 121.436 171.1343 168.0321 201.7188 238.1897 274.8055 314.1761

(Hnf/Hpf)V 1.10476451 1.07797523 1.01117157 1.0026325 1.0162503 1.05518168 1.04139384 1.07324153 1.08373015

M AN U TE D EP

(Hnf/Hpf)Re 1.075865026 1.076560447 1.082089197 1.065081018 1.079320978 1.090168255 1.127583933 1.08016342 1.087367899

RI PT

h_exp-0.05sK Nu_exp-0.05s 996.5051 0.117904 65.07888109 1682.359 0.117007 110.7126768 1891.455 0.114796 126.870515 2509.066 0.115016 167.9756577 2502.653 0.115023 167.5351509 3007.808 0.115881 199.861825 3511.754 0.114451 236.2631742 3969.847 0.116747 261.8304753 4510.361 0.116847 297.2255786

SC

Vel Pr Re^0.8 Pr^0.4 Pe 0.698716 13.9586495 13807.9887 77437.65 1.386518 14.5095547 24215.8436 154778.6 1.73881 16.1181284 30089.3486 197782.3 2.501792 15.937742 40097.8984 283984.9 2.4521 15.9363724 39464.3398 278393.2 2.944027 15.2837703 45035.2234 331804.9 3.632241 16.4055232 54567.068 414396.2 4.077402 14.6907251 57662.4105 456410 4.72499 14.6135602 64737.5239 528148.6

AC C

RE 5547.646 10667.36 12270.8 17818.39 17469.05 21709.62 25259.55 31067.9 36140.99

(Hnf/Hpf)Pe 1.16385706 1.129098234 1.043345026 1.036233883 1.050160357 1.096795616 1.071947184 1.121686405 1.133935255

0.05% 13nm0.05% 13nm0.05% 13nm 1.083228 1.054891 1.141168 1.030881 1.029528 1.079771 0.979 1.047661 1.01015 0.998521 1.060714 1.031985 0.992135 1.053709 1.02524 1.015733 1.049411 1.055791 1.017159 1.101343 1.047001 1.0871 1.094111 1.136171 1.091849 1.095514 1.14243

ACCEPTED MANUSCRIPT

K 0.111858 0.112378 0.110702 0.111413 0.1102 0.111389 0.111076 0.112173 0.111341

Nu_exp-0.5lNu_DB 75.93648 74.21862 112.1558 109.9809 140.3751 138.304 168.7731 166.8019 185.5256 186.3786 224.8539 215.7783 246.1604 233.3266 276.9776 269.4173 316.0861 296.4203

Nu_Gen 61.61831 100.0557 129.9734 162.225 183.2382 217.8415 237.7497 280.8886 311.7457

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe0.05% 50nm0.05% 50nm0.05% 50nm 1.099152 1.099152 1.11 1.05866 1.05866 1.069107784 1.113433 1.113433 1.128392 1.050546 1.050546 1.064659623 1.048862 1.048862 1.050909 1.013903 1.013903 1.015881482 1.071331 1.071331 1.078583 1.042452 1.042452 1.04950811 1.010491 1.010491 1.008793 1.001131 1.001131 0.999448778 1.102514 1.102514 1.109732 1.09573 1.09573 1.102903575 1.104432 1.104432 1.109397 1.126202 1.126202 1.131265382 1.115429 1.115429 1.128802 1.059624 1.059624 1.072328062 1.126469 1.126469 1.133281 1.095379 1.095379 1.102003867

RI PT

h_exp-05l 1103.125 1636.863 2018.149 2442.011 2655.192 3252.765 3550.96 4034.975 4570.553

M AN U

SC

Re^0.8 Pr^0.4 Pe 16196.9517 93294.23935 23464.2506 149681.3739 31871.4236 212550.6416 37151.5957 261122.9317 44053.3846 315206.0235 48115.4826 360595.7866 52801.0675 402532.3488 57990.7295 462121.5199 66256.6455 537361.1463

TE D

Pr 14.71455 14.16976 16.1123 15.22325 16.80809 15.25252 15.63185 14.3803 15.31377

EP

Vel 0.798449 1.286689 1.801282 2.22622 2.659148 3.073434 3.422132 3.9654 4.577204

AC C

RE 6340.269 10563.44 13191.82 17152.91 18753.23 23641.72 25750.78 32135.73 35090.06

ACCEPTED MANUSCRIPT

Nu_exp-0.2sNu_DB 61.4864 56.11831 101.3997 99.65 117.0625 113.4808 144.1866 145.8541 165.7678 163.2296 190.284 187.2735 221.3851 216.3877 265.5391 251.2614 288.2756 278.3376

Nu_Gen 43.53593 89.28494 103.3352 139.4522 158.355 186.1855 218.9646 259.7459 291.0525

(Hnf/Hpf)V 1.275443102 1.170830127 1.122631027 1.106681242 1.109358997 1.144029489 1.127668695 1.180545902 1.141684605

(Hnf/Hpf)Re 1.284093219 1.194488999 1.227873383 1.167623135 1.207360834 1.198318539 1.213244673 1.248157954 1.227576581

RI PT

h_exp-0.2s K 1047.632 0.131196 1714.759 0.130214 1913.001 0.125831 2396.274 0.127968 2714.888 0.126108 3173.68 0.128426 3644.946 0.126775 4407.746 0.127814 4746.987 0.126795

M AN U

SC

Re^0.8 Pr^0.4 Pe 11433.4124 62118.39 20582.3174 128792.6 25193.9201 160907.9 31208.9145 213539.6 36054.3463 252393.2 39768.2765 290018.6 47238.9297 355530.6 53855.0394 422040.8 60702.7119 486622

TE D

Pr 13.12195 13.42481 15.1415 14.239 15.01334 14.05985 14.72286 14.27954 14.69851

EP

Vel 0.621545 1.280633 1.547519 2.087761 2.432977 2.845743 3.444888 4.125298 4.719306

AC C

RE 4733.928 9593.626 10626.95 14996.81 16811.26 20627.44 24148.21 29555.64 33106.89

(Hnf/Hpf)Pe0.2% 13nm0.2% 13nm0.2% 13nm 1.459534 1.201224 1.20937 1.374602 1.333129 1.070038 1.09166 1.218366 1.244615 1.003994 1.098114 1.113087 1.243185 0.99789 1.052841 1.120974 1.232173 0.999596 1.087901 1.110258 1.288856 1.030742 1.079656 1.161228 1.257683 1.033747 1.112196 1.152933 1.325912 1.10662 1.169998 1.242883 1.274226 1.039619 1.117833 1.160312

ACCEPTED MANUSCRIPT

K 0.125829 0.125479 0.121532 0.123265 0.122087 0.123829 0.122335 0.124765 0.123391

Nu_exp-0.2lNu_DB 66.72749 62.98494 111.4692 100.0137 138.1021 128.3917 167.2666 155.0902 186.1079 171.6368 216.0257 196.3328 243.429 224.3843 286.1464 262.6416 310.7312 293.1144

Nu_Gen 50.56447 89.71656 119.5899 149.7068 167.8881 196.5216 228.0024 273.6766 308.9321

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.218923 1.195139 1.348647044 1.27567 1.25802 1.410155626 1.161001 1.237999 1.252011073 1.195828 1.22944 1.303905023 1.180646 1.243792 1.277970146 1.230182 1.250703 1.346278479 1.180497 1.248452 1.279710732 1.234643 1.233206 1.359003846 1.177607 1.207667 1.285088932

RI PT

h_exp-0.2l 1090.419 1816.499 2179.715 2677.686 2950.823 3474.048 3867.521 4636.501 4979.387

SC

Re^0.8 Pr^0.4 Pe 12902.1264 72085.25 20590.1435 129029.1 28553.2441 188025.5 33282.4345 231137 37719.4422 267611.9 41666.9541 307506 49399.4289 374652.4 54765.8073 435952.8 62745.437 511129.2

M AN U

13.241 13.352 15.18486 14.30861 14.8869 14.04574 14.93123 13.63922 14.24912

TE D

Pr

EP

Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561

AC C

RE 5444.095 9663.65 12382.43 16153.7 17976.33 21893.18 25091.86 31963.17 35870.93

0.2% 50nm0.2% 50nm0.2% 50nm 1.176226 1.153275 1.301406 1.193207 1.176698 1.318999 1.072299 1.143413 1.156355 1.109216 1.140394 1.209465 1.072065 1.129403 1.160439 1.117188 1.135824 1.222621 1.099887 1.163201 1.192325 1.151444 1.150105 1.267425 1.096179 1.12416 1.196228

ACCEPTED MANUSCRIPT

Nu_exp-0.3sNu_DB 67.6355 64.03218 102.797 88.42092 126.7817 114.3404 156.1554 137.6449 174.9715 159.5505 222.3501 196.6073 248.0932 223.3202 286.7741 251.8322 314.4038 271.8178

Nu_Gen 51.22818 77.12423 104.0727 130.0495 153.8867 195.9333 226.02 259.8369 282.7461

(Hnf/Hpf)V 1.185641083 1.329027593 1.195267188 1.252527278 1.180590009 1.229592283 1.185193237 1.248724405 1.252069608

M AN U TE D

(Hnf/Hpf)Re 1.254279776 1.374293179 1.332620188 1.353085775 1.31848137 1.355397074 1.340037919 1.359803446 1.388479936

RI PT

h_exp-0.3s K 1130.946 0.128753 1738.584 0.130228 2071.507 0.125812 2585.771 0.127504 2856.874 0.125723 3650.063 0.126402 4031.153 0.125114 4730.886 0.127026 5148.601 0.126093

SC

Pr Re^0.8 Pr^0.4 Pe 14.21163 13685.3757 76235.97 13.65727 18452.0874 111870.6 15.51732 25760.9561 164436.5 14.7233 30049.3645 201972.8 15.55859 36004.1494 249717 15.22936 43800.6874 320760.4 15.87839 51013.3747 384063.8 14.90663 55387.4257 432433.3 15.38466 60926.0106 483316.3

EP

Vel 0.749289 1.112027 1.580575 1.966943 2.398989 3.09715 3.671456 4.201294 4.654405

AC C

RE 5364.338 8191.285 10596.97 13717.9 16050.11 21061.97 24187.83 29009.45 31415.48

(Hnf/Hpf)Pe 1.337506581 1.51288134 1.324554106 1.402612492 1.307718957 1.367532613 1.307640674 1.395690271 1.389587622

0.3% 13nm 0.3% 13nm 0.3% 13nm 1.048587 1.109291 1.182897 1.16447 1.204131 1.32556 1.050256 1.170945 1.163857 1.086559 1.173792 1.216757 1.031577 1.152064 1.14266 1.079922 1.190414 1.201072 1.029352 1.163836 1.135699 1.089969 1.186926 1.218251 1.123628 1.246045 1.247039

ACCEPTED MANUSCRIPT

K 0.102582 0.126427 0.123222 0.124255 0.124042 0.124885 0.124227 0.126915 0.125735

Nu_exp-0.3lNu_DB 85.99118 67.21606 120.1099 102.416 150.6336 132.1555 188.1594 158.9348 188.3668 170.0043 239.7737 202.3768 255.5954 220.067 284.4845 248.5357 312.3335 275.2068

Nu_Gen 54.71687 92.06135 123.5585 153.6267 165.9727 203.0339 223.0541 257.2314 287.9402

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.178051 1.195691 1.306495845 1.32676 1.351873 1.474992721 1.224673 1.340405 1.334858122 1.294313 1.382152 1.420067544 1.207024 1.295278 1.322774477 1.308613 1.377506 1.441560308 1.269144 1.356096 1.392390322 1.304148 1.315634 1.454974513 1.270445 1.312958 1.406691714

RI PT

h_exp-0.3l 1145.606 1972.101 2410.568 3036.336 3034.471 3888.86 4123.626 4689.025 5100.145

M AN U

SC

Re^0.8 Pr^0.4 Pe 14105.5796 79778.58 21516.0126 135176.6 29731.7483 196826.1 34929.1963 243096.3 37532.066 265444.5 43867.2776 325060.5 48387.8929 365279.5 51687.2146 405986.3 58611.4662 470388.7

TE D

Pr 13.78509 13.8103 15.48003 14.88776 15.0009 14.54944 14.89987 13.57908 14.12815

EP

Vel 0.767586 1.304545 1.853157 2.307685 2.51621 3.101358 3.467357 3.935347 4.516705

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

0.3% 50nm0.3% 50nm0.3% 50nm 1.07283 1.088895 1.189802 1.197519 1.220186 1.331312 1.092166 1.195376 1.190429 1.155977 1.234428 1.268291 1.071911 1.150286 1.174704 1.167418 1.228876 1.28602 1.112423 1.188638 1.22045 1.157526 1.167722 1.291397 1.108565 1.145661 1.227452

ACCEPTED MANUSCRIPT

Nu_Gen 52.01392 109.5255 126.9408 149.2917 161.4681 182.3632 209.2581 236.2014 272.1572

(Hnf/Hpf)V 1.370130052 1.296301535 1.283756653 1.324405837 1.289846457 1.346430765 1.318479734 1.353072011 1.340044821

(Hnf/Hpf)Re 1.537441677 1.513339277 1.592212691 1.582594713 1.55742004 1.551848589 1.543975997 1.500626002 1.532098163

(Hnf/Hpf)Pe0.5% 13nm 1.599731 1.489318 1.447077 1.5095 1.465359 1.554578 1.51327 1.589468 1.552256

RI PT

Nu_exp-0.5sNu_DB 79.47883 64.97121 142.8185 119.4484 168.6683 136.156 193.8406 155.8581 203.7651 166.9166 227.138 184.7466 254.3888 208.6477 276.3672 231.0418 319.2169 262.5832

SC

h_exp-0.5s K 1389.448 0.134611 2445.348 0.13184 2818.264 0.128659 3284.955 0.130489 3438.53 0.129937 3912.965 0.13265 4349.012 0.131639 4865.766 0.135567 5521.925 0.133197

M AN U

Re^0.8 Pr^0.4 Pe 14144.63 78838.83 27114.33 174758.2 32807.68 216325.8 36219.19 248522.8 39187.97 273075.1 41381.97 298100.7 47507.67 351834.9 49632.14 380732.8 58319.86 459362

TE D

Pr 14.65539 15.71246 17.3558 16.33912 16.62016 15.36753 15.79295 14.33289 15.15173

EP

Vel 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418

AC C

RE 5379.509 11122.27 12464.18 15210.3 16430.35 19398.08 22277.97 26563.57 30317.47

1.058302489 1.099738065 1.108348345 1.135471921 1.101384653 1.176735755 1.143075549 1.138414644 1.156510411

0.5% 13nm0.5% 13nm 1.187536 1.235649 1.283865 1.263487 1.374658 1.249353 1.356829 1.294162 1.329863 1.251252 1.356264 1.358649 1.338573 1.311951 1.26256 1.337308 1.32226 1.339657

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

RE Vel Pr Re^0.8 Pr^0.4 Pe h_exp-0.5l K Nu_exp-0.5lNu_DB Nu_Gen (Hnf/Hpf)V (Hnf/Hpf)Re (Hnf/Hpf)Pe0.5% 50nm 4922.87805 0.699653673 14.59087644 13117.66821 71829.10536 1284.608568 0.128112 77.2099 60.41373 47.33686322 1.422590845 1.525969862 1.593409 9750.402834 1.369898174 14.33141543 22259.076 139737.0737 2046.873625 0.128373 122.7747 103.6243 93.08967541 1.324207643 1.407418926 1.490866 13180.32319 2.081466016 16.62645037 32865.51092 219141.9895 2971.416699 0.124479 183.8058 139.955 131.5091157 1.375573466 1.605362507 1.51001 18148.94292 2.845290758 16.48304217 42084.13815 299149.7916 3849.468936 0.124687 237.7217 180.1457 176.4150658 1.387762624 1.610164159 1.525059 20828.32383 3.363085294 17.08011992 48687.1522 355750.2688 4210.704877 0.123891 261.7002 204.0082 203.0491413 1.327945304 1.577544977 1.45223 24946.99404 3.911925305 16.48847461 54299.40348 411337.8779 5065.259953 0.124683 312.8139 232.3885 235.9882169 1.415484068 1.64262173 1.555391 29650.52862 4.804751989 17.15686942 64873.00241 508710.2476 5982.985833 0.123804 372.1111 271.0997 280.3462331 1.418393995 1.689827704 1.550024

0.5% 50nm 1.120787317 1.123796049 1.18396894 1.210760282 1.123654624 1.237425533 1.230750039

1.202234411 1.194413758 1.381750515 1.404795588 1.334855963 1.43599078 1.466274899

0.5% 50nm 1.255366 1.265231 1.29968 1.330545 1.228819 1.359733 1.344966

ACCEPTED MANUSCRIPT

7000 0.05% 13nm 6000

RI PT

0.05% 50nm 0.2% 13nm 0.2% 50nm

SC

4000

M AN U

3000

2000

0

200000

EP

0

TE D

1000

AC C

h (w/m2k)

5000

0.3% 13nm 0.3% 50nm 0.5% 13nm 0.5% 50nm Pure Kerosene

400000

600000

Pe

800000

1000000

ACCEPTED MANUSCRIPT

0.80 1.29 1.80 2.23 2.66 3.07 3.42 3.97 4.58 Vel 0.70 1.26 1.56 2.31 2.75 3.18 3.28 4.03 4.73

H 329.594 679.478 1183.04 1636.336 2059.792 2462.359 2849.026 3222.952 3586.306 3940.664 4287.216 4626.894 4960.442 5288.47 5611.485 5929.914 6244.122 888.0548 1536.526 1841.624 2463.771 2424.544 2806.421 3320.008 3641.717 4097.511 #VALUE! 888.0548 1447.366 1894.37 2244.16 2586.982 2904.682 3165.46 3561.468 3994.658 #VALUE! 891.291 1425.054 1690.124 2312.586 2655.211 2981.576 3059.105 3605.963 4104.4

RI PT

Nu 24.17023 50.30751 87.59046 121.1518 152.5038 182.3093 210.9375 238.6224 265.5246 291.7607 317.4189 342.5681 367.2635 391.5502 415.4657 439.0417 462.3052 65.75021 113.762 136.351 182.4138 179.5095 207.7831 245.8083 269.6272 303.3734 #VALUE! 65.75021 107.1607 140.2562 166.1542 191.5361 215.0582 234.3658 263.6856 295.7584 #VALUE! 65.98982 105.5088 125.1342 171.2203 196.5877 220.7513 226.4915 266.9799 303.8835

SC

Pe 23304.19 58260.47 116520.9 174781.4 233041.9 291302.3 349562.8 407823.3 466083.8 524344.2 582604.7 640865.2 699125.6 757386.1 815646.6 873907 932167.5 81415 161558.4 202607.8 291511.2 285721 343040.8 423232.1 475102.7 550560.2 #VALUE! 81415 149926.2 209887.1 259401.3 309846.4 358119.5 398750 462052.1 533340.2 #VALUE! 81786.03 147042.8 181992.3 269325.2 320094.7 370008.8 382074.3 469279.1 551717.6

M AN U

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

TE D

Vel

Re Pr 1536.202 3840.506 7681.011 11521.52 15362.02 19202.53 23043.03 26883.54 30724.04 34564.55 38405.06 42245.56 46086.07 49926.57 53767.08 57607.58 61448.09 5366.843 10649.86 13355.82 19216.29 18834.61 22613.1 27899.28 31318.57 36292.7 #VALUE! 5366.843 9883.071 13835.67 17099.62 20424.94 23607.08 26285.43 30458.28 35157.56 #VALUE! 5391.301 9692.999 11996.86 17753.8 21100.51 24390.82 25186.17 30934.68 36368.99

EP

0.20 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 0.70 1.39 1.74 2.50 2.45 2.94 3.63 4.08 4.72

AC C

V

#VALUE! 948.068 1494.933 1849.591 2302.415 2485.954 2743.895 2933.17 3570.648 3966.328 #VALUE! 808.6815 1441.913 1677.676 2131.788 2409.405 2731.215 3182.288 3675.899 4093.567 #VALUE! 880.739 1401.932 1848.404 2204.555 2460.67 2780.331 3225.505 3697.252 4162.99 939.1149 1287.928 1706.285 2032.511 2382.44 2922.599 3348.653 3729.974 4048.468 957.4169 1463.412 1937.89 2309.62 2475.124 2925.775 3198.882 3539.858

SC

#VALUE! 70.1935 110.6826 136.9409 170.4673 184.0562 203.1538 217.1674 264.3653 293.6608 #VALUE! 59.87353 106.7571 124.2126 157.8343 178.3886 202.215 235.6117 272.1579 303.0814 #VALUE! 65.20856 103.7969 136.853 163.2219 182.1842 205.8514 238.8114 273.7388 308.2214 69.53063 95.35623 126.3307 150.484 176.3922 216.3847 247.9291 276.1615 299.7424 70.88568 108.3488 143.4784 171.0007 183.2544 216.6199 236.8403 262.0856

M AN U

#VALUE! 88349.5 156110.4 203703.9 267845.4 294795.7 333514.1 362515.3 463541.5 528616.3 #VALUE! 72423.01 149220.6 180318.3 243267.8 283492.8 331588.7 401401.6 480683.5 549897.9 #VALUE! 80577.5 144066.6 203540.6 253691.5 291052.6 339059 408227.1 484176.3 561579.8 87307.82 129574.4 184170.1 229190.1 279532.4 360882.9 427801.6 489538.7 542335.7 89439.86 152006.8 215931.6 268893.6 293191.2 361373.2 404019.7 458550.3

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

#VALUE! 5823.962 10290.73 13428.08 17656.26 19432.81 21985.11 23896.86 30556.46 34846.16 #VALUE! 4774.094 9836.557 11886.51 16036.11 18687.72 21858.18 26460.23 31686.46 36249.04 #VALUE! 5311.635 9496.808 13417.31 16723.24 19186.06 22350.63 26910.16 31916.7 37019.1 5755.295 8541.493 12140.41 15108.11 18426.66 23789.25 28200.5 32270.18 35750.54 5895.838 10020.23 14234.12 17725.35 19327.04 23821.57 26632.81 30227.45

AC C

Vel 0.758229 1.339763 1.748217 2.298689 2.52998 2.862267 3.11116 3.978182 4.536663 Vel 0.62 1.28 1.55 2.09 2.43 2.85 3.44 4.13 4.72 Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561 0.75 1.11 1.58 1.97 2.40 3.10 3.67 4.20 4.65 0.77 1.30 1.85 2.31 2.52 3.10 3.47 3.94

RI PT

ACCEPTED MANUSCRIPT

3952.363 998.3795 1857.162 2161.295 2441.875 2624.52 2861.127 3247.374 3540.343 4056.825 889.0085 1521.774 2126.644 2730.868 3121.689 3522.993 4152.754 922.0801 1565.064 1679.369 2249.668 2227.969 2716.355 3066.233 3597.444 4107.391 1048.957 1534.846 1779.974 2223.705 2342.924 2874.383 3095.506 3686.68 3988.522 914.2035 1454.451 1555.335 2199.68 2436.893 2900.474 2917.17 3607.21 3976.339 1004.491 1568.337 1752.876

SC

292.6269 73.91849 137.5014 160.0189 180.7927 194.3154 211.8334 240.4306 262.1216 300.3611 65.82082 112.6698 157.4535 202.1893 231.1251 260.837 307.4635 68.26939 115.875 124.3379 166.562 164.9554 201.1147 227.0192 266.3492 304.1049 77.66317 113.6377 131.7865 164.6397 173.4665 212.8149 229.1865 272.9561 295.304 67.68622 107.6853 115.1546 162.8609 180.4238 214.7467 215.9827 267.0723 294.402 74.371 116.1173 129.7803

M AN U

526290.7 94248.47 204746.7 247484.1 288276.4 315476.6 351419.7 411689.8 458628.9 543735.4 81524.3 159621.8 242534.4 331535.9 391869.9 455821.2 559854.2 85332.71 165317.9 180545.8 260197.3 257064 329335 383187.4 467893.8 552220.2 100254 161337.7 194165.4 256449.1 273749 353456.2 387765.5 482446.4 532316.2 84422.53 150844.2 164034.4 252990.5 287541.3 357471.2 360045 469482.1 530284.5 94970.23 165750.2 190477.5

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

34692.86 6212.82 13496.81 16314.04 19003.06 20796.08 23165.44 27138.42 30232.63 35842.8 5374.048 10522.2 15987.76 21854.71 25831.9 30047.54 36905.35 5625.096 10897.69 11901.5 17152.1 16945.55 21709.62 25259.55 30843.37 36402.12 6608.704 10635.31 12799.3 16905.02 18045.42 23299.68 25561.34 31802.66 35090.06 5565.097 9943.588 10813.08 16677.03 18954.6 23564.35 23734.02 30948.06 34956.13 6260.398 10926.18 12556.2

AC C

4.52 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418 0.70 1.37 2.08 2.85 3.36 3.91 4.80

RI PT

ACCEPTED MANUSCRIPT

SC

2257.352 2365.024 2768.268 2927.392 3553.058 3961.52 803.2339 1420.566 1499.242 1965.644 2151.631 2579.476 2883.869 3438.884 3743.633 902.7711 1428.844 1703.752 2108.964 2296.182 2705.142 3015.379 3662.634 3992.714 885.5582 1219.384 1485.108 1828.159 2069.969 2588.067 2903.419 3362.635 3600.096 937.577 1421.87 1731.072 2127.646 2306.481 2735.096 2961.279 3457.199 3769.163 898.955 1552.341 1696.466 2012.643 2106.711

M AN U

167.1308 175.1027 204.9583 216.7396 263.0629 293.3049 59.4702 105.1765 111.0015 145.5332 159.3034 190.9804 213.5173 254.6097 277.1729 66.83978 105.7894 126.1432 156.1444 170.0058 200.2846 223.254 271.1758 295.6144 65.56537 90.28131 109.9551 135.3541 153.2573 191.6165 214.9647 248.9643 266.5456 69.41676 105.2731 128.1659 157.5277 170.7683 202.5023 219.2485 255.9657 279.063 66.55724 114.9329 125.6037 149.013 155.9776

TE D

261308.6 276980.4 337221.2 361622.8 460688.7 527815.4 71813.69 146464.2 156673 219804.1 246101.6 308723.1 354914.9 442259 491780.6 83104.93 147531.8 183828.5 240016.5 266939.4 327636.5 375259.8 478516.1 533015.7 81129 121012.5 154829 200757.6 234482 310008.9 357924.9 430035.5 468325 87129.13 146632.3 187520.5 242677.2 268436.8 332177.6 366862.9 445205.2 495976.2 82666.04 163639.6 182846.3 226393.1 239696.1

EP

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

AC C

17225.35 18258.43 22229.48 23838.02 30368.41 34793.37 4733.928 9654.858 10327.82 14489.39 16222.91 20350.89 23395.84 29153.53 32417.97 5478.242 9725.234 12117.9 15821.79 17596.53 21597.66 24736.97 31543.58 35136.17 5347.989 7977.094 10206.26 13233.86 15456.95 20435.66 23594.26 28347.76 30871.78 5743.516 9665.941 12361.27 15997.18 17695.24 21897.01 24183.45 29347.74 32694.54 5449.311 10787.06 12053.15 14923.74 15800.66

RI PT

ACCEPTED MANUSCRIPT

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

286166.1 327696.2 388219.8 452039.2 74314.91 142951.1 197652.6 268687.9 310975.8 374645.1 448248.3

179.7332 200.3137 229.4012 259.1042 61.12155 103.1534 133.6767 170.8961 192.0945 222.9614 257.3645

2427.565 2705.536 3098.406 3499.589 825.5378 1393.241 1805.503 2308.206 2594.523 3011.427 3476.091

AC C

EP

TE D

M AN U

SC

18863.95 21601.59 25591.28 29798.23 4898.807 9423.274 13029.18 17711.79 20499.4 24696.45 29548.34

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

Re

RePR 15.9 14473.49 15.9 76391.51

RI PT

M AN U TE D EP AC C

Pr 5000 40000

SC

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04601731 73.228819 60.5341941 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8333743 114.02112 103.854921 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6091968 145.27525 136.771494 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5438912 184.39553 180.878658 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9080838 216.74782 216.986307 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1383667 241.10514 246.006532 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2960579 247.95851 253.655111 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575419 277.97486 290.119402 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7894632 294.97439 309.411637 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718015 4523.427 42245.56 5.5 15.9 671704.4 0.105

0 550000

0 40000

0 5

1 1

ACCEPTED MANUSCRIPT

Nu_DB 65.30587 111.9013 130.5425 175.1432 172.3848 201.7167 234.2418 264.4811 297.8724

Nu_Gen 52.65631 101.9563 121.436 171.1343 168.0321 201.7188 238.1897 274.8055 314.1761

(Hnf/Hpf)V 1.10476451 1.07797523 1.01117157 1.0026325 1.0162503 1.05518168 1.04139384 1.07324153 1.08373015

M AN U TE D EP

(Hnf/Hpf)Re 1.075865026 1.076560447 1.082089197 1.065081018 1.079320978 1.090168255 1.127583933 1.08016342 1.087367899

RI PT

h_exp-0.05sK Nu_exp-0.05s 996.5051 0.117904 65.07888109 1682.359 0.117007 110.7126768 1891.455 0.114796 126.870515 2509.066 0.115016 167.9756577 2502.653 0.115023 167.5351509 3007.808 0.115881 199.861825 3511.754 0.114451 236.2631742 3969.847 0.116747 261.8304753 4510.361 0.116847 297.2255786

SC

Vel Pr Re^0.8 Pr^0.4 Pe 0.698716 13.9586495 13807.9887 77437.65 1.386518 14.5095547 24215.8436 154778.6 1.73881 16.1181284 30089.3486 197782.3 2.501792 15.937742 40097.8984 283984.9 2.4521 15.9363724 39464.3398 278393.2 2.944027 15.2837703 45035.2234 331804.9 3.632241 16.4055232 54567.068 414396.2 4.077402 14.6907251 57662.4105 456410 4.72499 14.6135602 64737.5239 528148.6

AC C

RE 5547.646 10667.36 12270.8 17818.39 17469.05 21709.62 25259.55 31067.9 36140.99

(Hnf/Hpf)Pe 1.16385706 1.129098234 1.043345026 1.036233883 1.050160357 1.096795616 1.071947184 1.121686405 1.133935255

0.05% 13nm0.05% 13nm0.05% 13nm 1.083228 1.054891 1.141168 1.030881 1.029528 1.079771 0.979 1.047661 1.01015 0.998521 1.060714 1.031985 0.992135 1.053709 1.02524 1.015733 1.049411 1.055791 1.017159 1.101343 1.047001 1.0871 1.094111 1.136171 1.091849 1.095514 1.14243

ACCEPTED MANUSCRIPT

K 0.111858 0.112378 0.110702 0.111413 0.1102 0.111389 0.111076 0.112173 0.111341

Nu_exp-0.5lNu_DB 75.93648 74.21862 112.1558 109.9809 140.3751 138.304 168.7731 166.8019 185.5256 186.3786 224.8539 215.7783 246.1604 233.3266 276.9776 269.4173 316.0861 296.4203

Nu_Gen 61.61831 100.0557 129.9734 162.225 183.2382 217.8415 237.7497 280.8886 311.7457

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe0.05% 50nm0.05% 50nm0.05% 50nm 1.099152 1.099152 1.11 1.05866 1.05866 1.069107784 1.113433 1.113433 1.128392 1.050546 1.050546 1.064659623 1.048862 1.048862 1.050909 1.013903 1.013903 1.015881482 1.071331 1.071331 1.078583 1.042452 1.042452 1.04950811 1.010491 1.010491 1.008793 1.001131 1.001131 0.999448778 1.102514 1.102514 1.109732 1.09573 1.09573 1.102903575 1.104432 1.104432 1.109397 1.126202 1.126202 1.131265382 1.115429 1.115429 1.128802 1.059624 1.059624 1.072328062 1.126469 1.126469 1.133281 1.095379 1.095379 1.102003867

RI PT

h_exp-05l 1103.125 1636.863 2018.149 2442.011 2655.192 3252.765 3550.96 4034.975 4570.553

M AN U

SC

Re^0.8 Pr^0.4 Pe 16196.9517 93294.23935 23464.2506 149681.3739 31871.4236 212550.6416 37151.5957 261122.9317 44053.3846 315206.0235 48115.4826 360595.7866 52801.0675 402532.3488 57990.7295 462121.5199 66256.6455 537361.1463

TE D

Pr 14.71455 14.16976 16.1123 15.22325 16.80809 15.25252 15.63185 14.3803 15.31377

EP

Vel 0.798449 1.286689 1.801282 2.22622 2.659148 3.073434 3.422132 3.9654 4.577204

AC C

RE 6340.269 10563.44 13191.82 17152.91 18753.23 23641.72 25750.78 32135.73 35090.06

ACCEPTED MANUSCRIPT

Nu_exp-0.2sNu_DB 61.4864 56.11831 101.3997 99.65 117.0625 113.4808 144.1866 145.8541 165.7678 163.2296 190.284 187.2735 221.3851 216.3877 265.5391 251.2614 288.2756 278.3376

Nu_Gen 43.53593 89.28494 103.3352 139.4522 158.355 186.1855 218.9646 259.7459 291.0525

(Hnf/Hpf)V 1.275443102 1.170830127 1.122631027 1.106681242 1.109358997 1.144029489 1.127668695 1.180545902 1.141684605

(Hnf/Hpf)Re 1.284093219 1.194488999 1.227873383 1.167623135 1.207360834 1.198318539 1.213244673 1.248157954 1.227576581

RI PT

h_exp-0.2s K 1047.632 0.131196 1714.759 0.130214 1913.001 0.125831 2396.274 0.127968 2714.888 0.126108 3173.68 0.128426 3644.946 0.126775 4407.746 0.127814 4746.987 0.126795

M AN U

SC

Re^0.8 Pr^0.4 Pe 11433.4124 62118.39 20582.3174 128792.6 25193.9201 160907.9 31208.9145 213539.6 36054.3463 252393.2 39768.2765 290018.6 47238.9297 355530.6 53855.0394 422040.8 60702.7119 486622

TE D

Pr 13.12195 13.42481 15.1415 14.239 15.01334 14.05985 14.72286 14.27954 14.69851

EP

Vel 0.621545 1.280633 1.547519 2.087761 2.432977 2.845743 3.444888 4.125298 4.719306

AC C

RE 4733.928 9593.626 10626.95 14996.81 16811.26 20627.44 24148.21 29555.64 33106.89

(Hnf/Hpf)Pe0.2% 13nm0.2% 13nm0.2% 13nm 1.459534 1.201224 1.20937 1.374602 1.333129 1.070038 1.09166 1.218366 1.244615 1.003994 1.098114 1.113087 1.243185 0.99789 1.052841 1.120974 1.232173 0.999596 1.087901 1.110258 1.288856 1.030742 1.079656 1.161228 1.257683 1.033747 1.112196 1.152933 1.325912 1.10662 1.169998 1.242883 1.274226 1.039619 1.117833 1.160312

ACCEPTED MANUSCRIPT

K 0.125829 0.125479 0.121532 0.123265 0.122087 0.123829 0.122335 0.124765 0.123391

Nu_exp-0.2lNu_DB 66.72749 62.98494 111.4692 100.0137 138.1021 128.3917 167.2666 155.0902 186.1079 171.6368 216.0257 196.3328 243.429 224.3843 286.1464 262.6416 310.7312 293.1144

Nu_Gen 50.56447 89.71656 119.5899 149.7068 167.8881 196.5216 228.0024 273.6766 308.9321

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.218923 1.195139 1.348647044 1.27567 1.25802 1.410155626 1.161001 1.237999 1.252011073 1.195828 1.22944 1.303905023 1.180646 1.243792 1.277970146 1.230182 1.250703 1.346278479 1.180497 1.248452 1.279710732 1.234643 1.233206 1.359003846 1.177607 1.207667 1.285088932

RI PT

h_exp-0.2l 1090.419 1816.499 2179.715 2677.686 2950.823 3474.048 3867.521 4636.501 4979.387

SC

Re^0.8 Pr^0.4 Pe 12902.1264 72085.25 20590.1435 129029.1 28553.2441 188025.5 33282.4345 231137 37719.4422 267611.9 41666.9541 307506 49399.4289 374652.4 54765.8073 435952.8 62745.437 511129.2

M AN U

13.241 13.352 15.18486 14.30861 14.8869 14.04574 14.93123 13.63922 14.24912

TE D

Pr

EP

Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561

AC C

RE 5444.095 9663.65 12382.43 16153.7 17976.33 21893.18 25091.86 31963.17 35870.93

0.2% 50nm0.2% 50nm0.2% 50nm 1.176226 1.153275 1.301406 1.193207 1.176698 1.318999 1.072299 1.143413 1.156355 1.109216 1.140394 1.209465 1.072065 1.129403 1.160439 1.117188 1.135824 1.222621 1.099887 1.163201 1.192325 1.151444 1.150105 1.267425 1.096179 1.12416 1.196228

ACCEPTED MANUSCRIPT

Nu_exp-0.3sNu_DB 67.6355 64.03218 102.797 88.42092 126.7817 114.3404 156.1554 137.6449 174.9715 159.5505 222.3501 196.6073 248.0932 223.3202 286.7741 251.8322 314.4038 271.8178

Nu_Gen 51.22818 77.12423 104.0727 130.0495 153.8867 195.9333 226.02 259.8369 282.7461

(Hnf/Hpf)V 1.185641083 1.329027593 1.195267188 1.252527278 1.180590009 1.229592283 1.185193237 1.248724405 1.252069608

M AN U TE D

(Hnf/Hpf)Re 1.254279776 1.374293179 1.332620188 1.353085775 1.31848137 1.355397074 1.340037919 1.359803446 1.388479936

RI PT

h_exp-0.3s K 1130.946 0.128753 1738.584 0.130228 2071.507 0.125812 2585.771 0.127504 2856.874 0.125723 3650.063 0.126402 4031.153 0.125114 4730.886 0.127026 5148.601 0.126093

SC

Pr Re^0.8 Pr^0.4 Pe 14.21163 13685.3757 76235.97 13.65727 18452.0874 111870.6 15.51732 25760.9561 164436.5 14.7233 30049.3645 201972.8 15.55859 36004.1494 249717 15.22936 43800.6874 320760.4 15.87839 51013.3747 384063.8 14.90663 55387.4257 432433.3 15.38466 60926.0106 483316.3

EP

Vel 0.749289 1.112027 1.580575 1.966943 2.398989 3.09715 3.671456 4.201294 4.654405

AC C

RE 5364.338 8191.285 10596.97 13717.9 16050.11 21061.97 24187.83 29009.45 31415.48

(Hnf/Hpf)Pe 1.337506581 1.51288134 1.324554106 1.402612492 1.307718957 1.367532613 1.307640674 1.395690271 1.389587622

0.3% 13nm 0.3% 13nm 0.3% 13nm 1.048587 1.109291 1.182897 1.16447 1.204131 1.32556 1.050256 1.170945 1.163857 1.086559 1.173792 1.216757 1.031577 1.152064 1.14266 1.079922 1.190414 1.201072 1.029352 1.163836 1.135699 1.089969 1.186926 1.218251 1.123628 1.246045 1.247039

ACCEPTED MANUSCRIPT

K 0.102582 0.126427 0.123222 0.124255 0.124042 0.124885 0.124227 0.126915 0.125735

Nu_exp-0.3lNu_DB 85.99118 67.21606 120.1099 102.416 150.6336 132.1555 188.1594 158.9348 188.3668 170.0043 239.7737 202.3768 255.5954 220.067 284.4845 248.5357 312.3335 275.2068

Nu_Gen 54.71687 92.06135 123.5585 153.6267 165.9727 203.0339 223.0541 257.2314 287.9402

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.178051 1.195691 1.306495845 1.32676 1.351873 1.474992721 1.224673 1.340405 1.334858122 1.294313 1.382152 1.420067544 1.207024 1.295278 1.322774477 1.308613 1.377506 1.441560308 1.269144 1.356096 1.392390322 1.304148 1.315634 1.454974513 1.270445 1.312958 1.406691714

RI PT

h_exp-0.3l 1145.606 1972.101 2410.568 3036.336 3034.471 3888.86 4123.626 4689.025 5100.145

M AN U

SC

Re^0.8 Pr^0.4 Pe 14105.5796 79778.58 21516.0126 135176.6 29731.7483 196826.1 34929.1963 243096.3 37532.066 265444.5 43867.2776 325060.5 48387.8929 365279.5 51687.2146 405986.3 58611.4662 470388.7

TE D

Pr 13.78509 13.8103 15.48003 14.88776 15.0009 14.54944 14.89987 13.57908 14.12815

EP

Vel 0.767586 1.304545 1.853157 2.307685 2.51621 3.101358 3.467357 3.935347 4.516705

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

0.3% 50nm0.3% 50nm0.3% 50nm 1.07283 1.088895 1.189802 1.197519 1.220186 1.331312 1.092166 1.195376 1.190429 1.155977 1.234428 1.268291 1.071911 1.150286 1.174704 1.167418 1.228876 1.28602 1.112423 1.188638 1.22045 1.157526 1.167722 1.291397 1.108565 1.145661 1.227452

ACCEPTED MANUSCRIPT

Nu_Gen 52.01392 109.5255 126.9408 149.2917 161.4681 182.3632 209.2581 236.2014 272.1572

(Hnf/Hpf)V 1.370130052 1.296301535 1.283756653 1.324405837 1.289846457 1.346430765 1.318479734 1.353072011 1.340044821

(Hnf/Hpf)Re 1.537441677 1.513339277 1.592212691 1.582594713 1.55742004 1.551848589 1.543975997 1.500626002 1.532098163

(Hnf/Hpf)Pe0.5% 13nm 1.599731 1.489318 1.447077 1.5095 1.465359 1.554578 1.51327 1.589468 1.552256

RI PT

Nu_exp-0.5sNu_DB 79.47883 64.97121 142.8185 119.4484 168.6683 136.156 193.8406 155.8581 203.7651 166.9166 227.138 184.7466 254.3888 208.6477 276.3672 231.0418 319.2169 262.5832

SC

h_exp-0.5s K 1389.448 0.134611 2445.348 0.13184 2818.264 0.128659 3284.955 0.130489 3438.53 0.129937 3912.965 0.13265 4349.012 0.131639 4865.766 0.135567 5521.925 0.133197

M AN U

Re^0.8 Pr^0.4 Pe 14144.63 78838.83 27114.33 174758.2 32807.68 216325.8 36219.19 248522.8 39187.97 273075.1 41381.97 298100.7 47507.67 351834.9 49632.14 380732.8 58319.86 459362

TE D

Pr 14.65539 15.71246 17.3558 16.33912 16.62016 15.36753 15.79295 14.33289 15.15173

EP

Vel 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418

AC C

RE 5379.509 11122.27 12464.18 15210.3 16430.35 19398.08 22277.97 26563.57 30317.47

1.058302489 1.099738065 1.108348345 1.135471921 1.101384653 1.176735755 1.143075549 1.138414644 1.156510411

0.5% 13nm0.5% 13nm 1.187536 1.235649 1.283865 1.263487 1.374658 1.249353 1.356829 1.294162 1.329863 1.251252 1.356264 1.358649 1.338573 1.311951 1.26256 1.337308 1.32226 1.339657

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

RE Vel Pr Re^0.8 Pr^0.4 Pe h_exp-0.5l K Nu_exp-0.5lNu_DB Nu_Gen (Hnf/Hpf)V (Hnf/Hpf)Re (Hnf/Hpf)Pe0.5% 50nm 4922.87805 0.699653673 14.59087644 13117.66821 71829.10536 1284.608568 0.128112 77.2099 60.41373 47.33686322 1.422590845 1.525969862 1.593409 9750.402834 1.369898174 14.33141543 22259.076 139737.0737 2046.873625 0.128373 122.7747 103.6243 93.08967541 1.324207643 1.407418926 1.490866 13180.32319 2.081466016 16.62645037 32865.51092 219141.9895 2971.416699 0.124479 183.8058 139.955 131.5091157 1.375573466 1.605362507 1.51001 18148.94292 2.845290758 16.48304217 42084.13815 299149.7916 3849.468936 0.124687 237.7217 180.1457 176.4150658 1.387762624 1.610164159 1.525059 20828.32383 3.363085294 17.08011992 48687.1522 355750.2688 4210.704877 0.123891 261.7002 204.0082 203.0491413 1.327945304 1.577544977 1.45223 24946.99404 3.911925305 16.48847461 54299.40348 411337.8779 5065.259953 0.124683 312.8139 232.3885 235.9882169 1.415484068 1.64262173 1.555391 29650.52862 4.804751989 17.15686942 64873.00241 508710.2476 5982.985833 0.123804 372.1111 271.0997 280.3462331 1.418393995 1.689827704 1.550024

0.5% 50nm 1.120787317 1.123796049 1.18396894 1.210760282 1.123654624 1.237425533 1.230750039

1.202234411 1.194413758 1.381750515 1.404795588 1.334855963 1.43599078 1.466274899

0.5% 50nm 1.255366 1.265231 1.29968 1.330545 1.228819 1.359733 1.344966

ACCEPTED MANUSCRIPT

1.8

0.5% 50nm 1.7

RI PT

0.5% 13nm 1.6

0.3% 50nm 0.3% 13nm

SC

1.4 1.3

M AN U

hnf / hbf

1.5

1.2 1.1

0.9

10000

AC C

EP

0

TE D

1

20000

30000

Re

0.2% 50nm 0.2% 13nm 0.05% 50nm 0.05% 13nm

40000

50000

60000

ACCEPTED MANUSCRIPT

0.80 1.29 1.80 2.23 2.66 3.07 3.42 3.97 4.58 Vel 0.70 1.26 1.56 2.31 2.75 3.18 3.28 4.03 4.73

H 329.594 679.478 1183.04 1636.336 2059.792 2462.359 2849.026 3222.952 3586.306 3940.664 4287.216 4626.894 4960.442 5288.47 5611.485 5929.914 6244.122 888.0548 1536.526 1841.624 2463.771 2424.544 2806.421 3320.008 3641.717 4097.511 #VALUE! 888.0548 1447.366 1894.37 2244.16 2586.982 2904.682 3165.46 3561.468 3994.658 #VALUE! 891.291 1425.054 1690.124 2312.586 2655.211 2981.576 3059.105 3605.963 4104.4

RI PT

Nu 24.17023 50.30751 87.59046 121.1518 152.5038 182.3093 210.9375 238.6224 265.5246 291.7607 317.4189 342.5681 367.2635 391.5502 415.4657 439.0417 462.3052 65.75021 113.762 136.351 182.4138 179.5095 207.7831 245.8083 269.6272 303.3734 #VALUE! 65.75021 107.1607 140.2562 166.1542 191.5361 215.0582 234.3658 263.6856 295.7584 #VALUE! 65.98982 105.5088 125.1342 171.2203 196.5877 220.7513 226.4915 266.9799 303.8835

SC

Pe 23304.19 58260.47 116520.9 174781.4 233041.9 291302.3 349562.8 407823.3 466083.8 524344.2 582604.7 640865.2 699125.6 757386.1 815646.6 873907 932167.5 81415 161558.4 202607.8 291511.2 285721 343040.8 423232.1 475102.7 550560.2 #VALUE! 81415 149926.2 209887.1 259401.3 309846.4 358119.5 398750 462052.1 533340.2 #VALUE! 81786.03 147042.8 181992.3 269325.2 320094.7 370008.8 382074.3 469279.1 551717.6

M AN U

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

TE D

Vel

Re Pr 1536.202 3840.506 7681.011 11521.52 15362.02 19202.53 23043.03 26883.54 30724.04 34564.55 38405.06 42245.56 46086.07 49926.57 53767.08 57607.58 61448.09 5366.843 10649.86 13355.82 19216.29 18834.61 22613.1 27899.28 31318.57 36292.7 #VALUE! 5366.843 9883.071 13835.67 17099.62 20424.94 23607.08 26285.43 30458.28 35157.56 #VALUE! 5391.301 9692.999 11996.86 17753.8 21100.51 24390.82 25186.17 30934.68 36368.99

EP

0.20 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 0.70 1.39 1.74 2.50 2.45 2.94 3.63 4.08 4.72

AC C

V

#VALUE! 948.068 1494.933 1849.591 2302.415 2485.954 2743.895 2933.17 3570.648 3966.328 #VALUE! 808.6815 1441.913 1677.676 2131.788 2409.405 2731.215 3182.288 3675.899 4093.567 #VALUE! 880.739 1401.932 1848.404 2204.555 2460.67 2780.331 3225.505 3697.252 4162.99 939.1149 1287.928 1706.285 2032.511 2382.44 2922.599 3348.653 3729.974 4048.468 957.4169 1463.412 1937.89 2309.62 2475.124 2925.775 3198.882 3539.858

SC

#VALUE! 70.1935 110.6826 136.9409 170.4673 184.0562 203.1538 217.1674 264.3653 293.6608 #VALUE! 59.87353 106.7571 124.2126 157.8343 178.3886 202.215 235.6117 272.1579 303.0814 #VALUE! 65.20856 103.7969 136.853 163.2219 182.1842 205.8514 238.8114 273.7388 308.2214 69.53063 95.35623 126.3307 150.484 176.3922 216.3847 247.9291 276.1615 299.7424 70.88568 108.3488 143.4784 171.0007 183.2544 216.6199 236.8403 262.0856

M AN U

#VALUE! 88349.5 156110.4 203703.9 267845.4 294795.7 333514.1 362515.3 463541.5 528616.3 #VALUE! 72423.01 149220.6 180318.3 243267.8 283492.8 331588.7 401401.6 480683.5 549897.9 #VALUE! 80577.5 144066.6 203540.6 253691.5 291052.6 339059 408227.1 484176.3 561579.8 87307.82 129574.4 184170.1 229190.1 279532.4 360882.9 427801.6 489538.7 542335.7 89439.86 152006.8 215931.6 268893.6 293191.2 361373.2 404019.7 458550.3

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

#VALUE! 5823.962 10290.73 13428.08 17656.26 19432.81 21985.11 23896.86 30556.46 34846.16 #VALUE! 4774.094 9836.557 11886.51 16036.11 18687.72 21858.18 26460.23 31686.46 36249.04 #VALUE! 5311.635 9496.808 13417.31 16723.24 19186.06 22350.63 26910.16 31916.7 37019.1 5755.295 8541.493 12140.41 15108.11 18426.66 23789.25 28200.5 32270.18 35750.54 5895.838 10020.23 14234.12 17725.35 19327.04 23821.57 26632.81 30227.45

AC C

Vel 0.758229 1.339763 1.748217 2.298689 2.52998 2.862267 3.11116 3.978182 4.536663 Vel 0.62 1.28 1.55 2.09 2.43 2.85 3.44 4.13 4.72 Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561 0.75 1.11 1.58 1.97 2.40 3.10 3.67 4.20 4.65 0.77 1.30 1.85 2.31 2.52 3.10 3.47 3.94

RI PT

ACCEPTED MANUSCRIPT

3952.363 998.3795 1857.162 2161.295 2441.875 2624.52 2861.127 3247.374 3540.343 4056.825 889.0085 1521.774 2126.644 2730.868 3121.689 3522.993 4152.754 922.0801 1565.064 1679.369 2249.668 2227.969 2716.355 3066.233 3597.444 4107.391 1048.957 1534.846 1779.974 2223.705 2342.924 2874.383 3095.506 3686.68 3988.522 914.2035 1454.451 1555.335 2199.68 2436.893 2900.474 2917.17 3607.21 3976.339 1004.491 1568.337 1752.876

SC

292.6269 73.91849 137.5014 160.0189 180.7927 194.3154 211.8334 240.4306 262.1216 300.3611 65.82082 112.6698 157.4535 202.1893 231.1251 260.837 307.4635 68.26939 115.875 124.3379 166.562 164.9554 201.1147 227.0192 266.3492 304.1049 77.66317 113.6377 131.7865 164.6397 173.4665 212.8149 229.1865 272.9561 295.304 67.68622 107.6853 115.1546 162.8609 180.4238 214.7467 215.9827 267.0723 294.402 74.371 116.1173 129.7803

M AN U

526290.7 94248.47 204746.7 247484.1 288276.4 315476.6 351419.7 411689.8 458628.9 543735.4 81524.3 159621.8 242534.4 331535.9 391869.9 455821.2 559854.2 85332.71 165317.9 180545.8 260197.3 257064 329335 383187.4 467893.8 552220.2 100254 161337.7 194165.4 256449.1 273749 353456.2 387765.5 482446.4 532316.2 84422.53 150844.2 164034.4 252990.5 287541.3 357471.2 360045 469482.1 530284.5 94970.23 165750.2 190477.5

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

34692.86 6212.82 13496.81 16314.04 19003.06 20796.08 23165.44 27138.42 30232.63 35842.8 5374.048 10522.2 15987.76 21854.71 25831.9 30047.54 36905.35 5625.096 10897.69 11901.5 17152.1 16945.55 21709.62 25259.55 30843.37 36402.12 6608.704 10635.31 12799.3 16905.02 18045.42 23299.68 25561.34 31802.66 35090.06 5565.097 9943.588 10813.08 16677.03 18954.6 23564.35 23734.02 30948.06 34956.13 6260.398 10926.18 12556.2

AC C

4.52 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418 0.70 1.37 2.08 2.85 3.36 3.91 4.80

RI PT

ACCEPTED MANUSCRIPT

SC

2257.352 2365.024 2768.268 2927.392 3553.058 3961.52 803.2339 1420.566 1499.242 1965.644 2151.631 2579.476 2883.869 3438.884 3743.633 902.7711 1428.844 1703.752 2108.964 2296.182 2705.142 3015.379 3662.634 3992.714 885.5582 1219.384 1485.108 1828.159 2069.969 2588.067 2903.419 3362.635 3600.096 937.577 1421.87 1731.072 2127.646 2306.481 2735.096 2961.279 3457.199 3769.163 898.955 1552.341 1696.466 2012.643 2106.711

M AN U

167.1308 175.1027 204.9583 216.7396 263.0629 293.3049 59.4702 105.1765 111.0015 145.5332 159.3034 190.9804 213.5173 254.6097 277.1729 66.83978 105.7894 126.1432 156.1444 170.0058 200.2846 223.254 271.1758 295.6144 65.56537 90.28131 109.9551 135.3541 153.2573 191.6165 214.9647 248.9643 266.5456 69.41676 105.2731 128.1659 157.5277 170.7683 202.5023 219.2485 255.9657 279.063 66.55724 114.9329 125.6037 149.013 155.9776

TE D

261308.6 276980.4 337221.2 361622.8 460688.7 527815.4 71813.69 146464.2 156673 219804.1 246101.6 308723.1 354914.9 442259 491780.6 83104.93 147531.8 183828.5 240016.5 266939.4 327636.5 375259.8 478516.1 533015.7 81129 121012.5 154829 200757.6 234482 310008.9 357924.9 430035.5 468325 87129.13 146632.3 187520.5 242677.2 268436.8 332177.6 366862.9 445205.2 495976.2 82666.04 163639.6 182846.3 226393.1 239696.1

EP

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

AC C

17225.35 18258.43 22229.48 23838.02 30368.41 34793.37 4733.928 9654.858 10327.82 14489.39 16222.91 20350.89 23395.84 29153.53 32417.97 5478.242 9725.234 12117.9 15821.79 17596.53 21597.66 24736.97 31543.58 35136.17 5347.989 7977.094 10206.26 13233.86 15456.95 20435.66 23594.26 28347.76 30871.78 5743.516 9665.941 12361.27 15997.18 17695.24 21897.01 24183.45 29347.74 32694.54 5449.311 10787.06 12053.15 14923.74 15800.66

RI PT

ACCEPTED MANUSCRIPT

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

286166.1 327696.2 388219.8 452039.2 74314.91 142951.1 197652.6 268687.9 310975.8 374645.1 448248.3

179.7332 200.3137 229.4012 259.1042 61.12155 103.1534 133.6767 170.8961 192.0945 222.9614 257.3645

2427.565 2705.536 3098.406 3499.589 825.5378 1393.241 1805.503 2308.206 2594.523 3011.427 3476.091

AC C

EP

TE D

M AN U

SC

18863.95 21601.59 25591.28 29798.23 4898.807 9423.274 13029.18 17711.79 20499.4 24696.45 29548.34

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

Re

RePR 15.9 14473.49 15.9 76391.51

RI PT

M AN U TE D EP AC C

Pr 5000 40000

SC

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04601731 73.228819 60.5341941 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8333743 114.02112 103.854921 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6091968 145.27525 136.771494 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5438912 184.39553 180.878658 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9080838 216.74782 216.986307 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1383667 241.10514 246.006532 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2960579 247.95851 253.655111 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575419 277.97486 290.119402 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7894632 294.97439 309.411637 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718015 4523.427 42245.56 5.5 15.9 671704.4 0.105

0 550000

0 40000

0 5

1 1

ACCEPTED MANUSCRIPT

Nu_DB 65.30587 111.9013 130.5425 175.1432 172.3848 201.7167 234.2418 264.4811 297.8724

Nu_Gen 52.65631 101.9563 121.436 171.1343 168.0321 201.7188 238.1897 274.8055 314.1761

(Hnf/Hpf)V 1.10476451 1.07797523 1.01117157 1.0026325 1.0162503 1.05518168 1.04139384 1.07324153 1.08373015

M AN U TE D EP

(Hnf/Hpf)Re 1.075865026 1.076560447 1.082089197 1.065081018 1.079320978 1.090168255 1.127583933 1.08016342 1.087367899

RI PT

h_exp-0.05sK Nu_exp-0.05s 996.5051 0.117904 65.07888109 1682.359 0.117007 110.7126768 1891.455 0.114796 126.870515 2509.066 0.115016 167.9756577 2502.653 0.115023 167.5351509 3007.808 0.115881 199.861825 3511.754 0.114451 236.2631742 3969.847 0.116747 261.8304753 4510.361 0.116847 297.2255786

SC

Vel Pr Re^0.8 Pr^0.4 Pe 0.698716 13.9586495 13807.9887 77437.65 1.386518 14.5095547 24215.8436 154778.6 1.73881 16.1181284 30089.3486 197782.3 2.501792 15.937742 40097.8984 283984.9 2.4521 15.9363724 39464.3398 278393.2 2.944027 15.2837703 45035.2234 331804.9 3.632241 16.4055232 54567.068 414396.2 4.077402 14.6907251 57662.4105 456410 4.72499 14.6135602 64737.5239 528148.6

AC C

RE 5547.646 10667.36 12270.8 17818.39 17469.05 21709.62 25259.55 31067.9 36140.99

(Hnf/Hpf)Pe 1.16385706 1.129098234 1.043345026 1.036233883 1.050160357 1.096795616 1.071947184 1.121686405 1.133935255

0.05% 13nm0.05% 13nm0.05% 13nm 1.083228 1.054891 1.141168 1.030881 1.029528 1.079771 0.979 1.047661 1.01015 0.998521 1.060714 1.031985 0.992135 1.053709 1.02524 1.015733 1.049411 1.055791 1.017159 1.101343 1.047001 1.0871 1.094111 1.136171 1.091849 1.095514 1.14243

ACCEPTED MANUSCRIPT

K 0.111858 0.112378 0.110702 0.111413 0.1102 0.111389 0.111076 0.112173 0.111341

Nu_exp-0.5lNu_DB 75.93648 74.21862 112.1558 109.9809 140.3751 138.304 168.7731 166.8019 185.5256 186.3786 224.8539 215.7783 246.1604 233.3266 276.9776 269.4173 316.0861 296.4203

Nu_Gen 61.61831 100.0557 129.9734 162.225 183.2382 217.8415 237.7497 280.8886 311.7457

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe0.05% 50nm0.05% 50nm0.05% 50nm 1.099152 1.099152 1.11 1.05866 1.05866 1.069107784 1.113433 1.113433 1.128392 1.050546 1.050546 1.064659623 1.048862 1.048862 1.050909 1.013903 1.013903 1.015881482 1.071331 1.071331 1.078583 1.042452 1.042452 1.04950811 1.010491 1.010491 1.008793 1.001131 1.001131 0.999448778 1.102514 1.102514 1.109732 1.09573 1.09573 1.102903575 1.104432 1.104432 1.109397 1.126202 1.126202 1.131265382 1.115429 1.115429 1.128802 1.059624 1.059624 1.072328062 1.126469 1.126469 1.133281 1.095379 1.095379 1.102003867

RI PT

h_exp-05l 1103.125 1636.863 2018.149 2442.011 2655.192 3252.765 3550.96 4034.975 4570.553

M AN U

SC

Re^0.8 Pr^0.4 Pe 16196.9517 93294.23935 23464.2506 149681.3739 31871.4236 212550.6416 37151.5957 261122.9317 44053.3846 315206.0235 48115.4826 360595.7866 52801.0675 402532.3488 57990.7295 462121.5199 66256.6455 537361.1463

TE D

Pr 14.71455 14.16976 16.1123 15.22325 16.80809 15.25252 15.63185 14.3803 15.31377

EP

Vel 0.798449 1.286689 1.801282 2.22622 2.659148 3.073434 3.422132 3.9654 4.577204

AC C

RE 6340.269 10563.44 13191.82 17152.91 18753.23 23641.72 25750.78 32135.73 35090.06

ACCEPTED MANUSCRIPT

Nu_exp-0.2sNu_DB 61.4864 56.11831 101.3997 99.65 117.0625 113.4808 144.1866 145.8541 165.7678 163.2296 190.284 187.2735 221.3851 216.3877 265.5391 251.2614 288.2756 278.3376

Nu_Gen 43.53593 89.28494 103.3352 139.4522 158.355 186.1855 218.9646 259.7459 291.0525

(Hnf/Hpf)V 1.275443102 1.170830127 1.122631027 1.106681242 1.109358997 1.144029489 1.127668695 1.180545902 1.141684605

(Hnf/Hpf)Re 1.284093219 1.194488999 1.227873383 1.167623135 1.207360834 1.198318539 1.213244673 1.248157954 1.227576581

RI PT

h_exp-0.2s K 1047.632 0.131196 1714.759 0.130214 1913.001 0.125831 2396.274 0.127968 2714.888 0.126108 3173.68 0.128426 3644.946 0.126775 4407.746 0.127814 4746.987 0.126795

M AN U

SC

Re^0.8 Pr^0.4 Pe 11433.4124 62118.39 20582.3174 128792.6 25193.9201 160907.9 31208.9145 213539.6 36054.3463 252393.2 39768.2765 290018.6 47238.9297 355530.6 53855.0394 422040.8 60702.7119 486622

TE D

Pr 13.12195 13.42481 15.1415 14.239 15.01334 14.05985 14.72286 14.27954 14.69851

EP

Vel 0.621545 1.280633 1.547519 2.087761 2.432977 2.845743 3.444888 4.125298 4.719306

AC C

RE 4733.928 9593.626 10626.95 14996.81 16811.26 20627.44 24148.21 29555.64 33106.89

(Hnf/Hpf)Pe0.2% 13nm0.2% 13nm0.2% 13nm 1.459534 1.201224 1.20937 1.374602 1.333129 1.070038 1.09166 1.218366 1.244615 1.003994 1.098114 1.113087 1.243185 0.99789 1.052841 1.120974 1.232173 0.999596 1.087901 1.110258 1.288856 1.030742 1.079656 1.161228 1.257683 1.033747 1.112196 1.152933 1.325912 1.10662 1.169998 1.242883 1.274226 1.039619 1.117833 1.160312

ACCEPTED MANUSCRIPT

K 0.125829 0.125479 0.121532 0.123265 0.122087 0.123829 0.122335 0.124765 0.123391

Nu_exp-0.2lNu_DB 66.72749 62.98494 111.4692 100.0137 138.1021 128.3917 167.2666 155.0902 186.1079 171.6368 216.0257 196.3328 243.429 224.3843 286.1464 262.6416 310.7312 293.1144

Nu_Gen 50.56447 89.71656 119.5899 149.7068 167.8881 196.5216 228.0024 273.6766 308.9321

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.218923 1.195139 1.348647044 1.27567 1.25802 1.410155626 1.161001 1.237999 1.252011073 1.195828 1.22944 1.303905023 1.180646 1.243792 1.277970146 1.230182 1.250703 1.346278479 1.180497 1.248452 1.279710732 1.234643 1.233206 1.359003846 1.177607 1.207667 1.285088932

RI PT

h_exp-0.2l 1090.419 1816.499 2179.715 2677.686 2950.823 3474.048 3867.521 4636.501 4979.387

SC

Re^0.8 Pr^0.4 Pe 12902.1264 72085.25 20590.1435 129029.1 28553.2441 188025.5 33282.4345 231137 37719.4422 267611.9 41666.9541 307506 49399.4289 374652.4 54765.8073 435952.8 62745.437 511129.2

M AN U

13.241 13.352 15.18486 14.30861 14.8869 14.04574 14.93123 13.63922 14.24912

TE D

Pr

EP

Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561

AC C

RE 5444.095 9663.65 12382.43 16153.7 17976.33 21893.18 25091.86 31963.17 35870.93

0.2% 50nm0.2% 50nm0.2% 50nm 1.176226 1.153275 1.301406 1.193207 1.176698 1.318999 1.072299 1.143413 1.156355 1.109216 1.140394 1.209465 1.072065 1.129403 1.160439 1.117188 1.135824 1.222621 1.099887 1.163201 1.192325 1.151444 1.150105 1.267425 1.096179 1.12416 1.196228

ACCEPTED MANUSCRIPT

Nu_exp-0.3sNu_DB 67.6355 64.03218 102.797 88.42092 126.7817 114.3404 156.1554 137.6449 174.9715 159.5505 222.3501 196.6073 248.0932 223.3202 286.7741 251.8322 314.4038 271.8178

Nu_Gen 51.22818 77.12423 104.0727 130.0495 153.8867 195.9333 226.02 259.8369 282.7461

(Hnf/Hpf)V 1.185641083 1.329027593 1.195267188 1.252527278 1.180590009 1.229592283 1.185193237 1.248724405 1.252069608

M AN U TE D

(Hnf/Hpf)Re 1.254279776 1.374293179 1.332620188 1.353085775 1.31848137 1.355397074 1.340037919 1.359803446 1.388479936

RI PT

h_exp-0.3s K 1130.946 0.128753 1738.584 0.130228 2071.507 0.125812 2585.771 0.127504 2856.874 0.125723 3650.063 0.126402 4031.153 0.125114 4730.886 0.127026 5148.601 0.126093

SC

Pr Re^0.8 Pr^0.4 Pe 14.21163 13685.3757 76235.97 13.65727 18452.0874 111870.6 15.51732 25760.9561 164436.5 14.7233 30049.3645 201972.8 15.55859 36004.1494 249717 15.22936 43800.6874 320760.4 15.87839 51013.3747 384063.8 14.90663 55387.4257 432433.3 15.38466 60926.0106 483316.3

EP

Vel 0.749289 1.112027 1.580575 1.966943 2.398989 3.09715 3.671456 4.201294 4.654405

AC C

RE 5364.338 8191.285 10596.97 13717.9 16050.11 21061.97 24187.83 29009.45 31415.48

(Hnf/Hpf)Pe 1.337506581 1.51288134 1.324554106 1.402612492 1.307718957 1.367532613 1.307640674 1.395690271 1.389587622

0.3% 13nm 0.3% 13nm 0.3% 13nm 1.048587 1.109291 1.182897 1.16447 1.204131 1.32556 1.050256 1.170945 1.163857 1.086559 1.173792 1.216757 1.031577 1.152064 1.14266 1.079922 1.190414 1.201072 1.029352 1.163836 1.135699 1.089969 1.186926 1.218251 1.123628 1.246045 1.247039

ACCEPTED MANUSCRIPT

K 0.102582 0.126427 0.123222 0.124255 0.124042 0.124885 0.124227 0.126915 0.125735

Nu_exp-0.3lNu_DB 85.99118 67.21606 120.1099 102.416 150.6336 132.1555 188.1594 158.9348 188.3668 170.0043 239.7737 202.3768 255.5954 220.067 284.4845 248.5357 312.3335 275.2068

Nu_Gen 54.71687 92.06135 123.5585 153.6267 165.9727 203.0339 223.0541 257.2314 287.9402

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.178051 1.195691 1.306495845 1.32676 1.351873 1.474992721 1.224673 1.340405 1.334858122 1.294313 1.382152 1.420067544 1.207024 1.295278 1.322774477 1.308613 1.377506 1.441560308 1.269144 1.356096 1.392390322 1.304148 1.315634 1.454974513 1.270445 1.312958 1.406691714

RI PT

h_exp-0.3l 1145.606 1972.101 2410.568 3036.336 3034.471 3888.86 4123.626 4689.025 5100.145

M AN U

SC

Re^0.8 Pr^0.4 Pe 14105.5796 79778.58 21516.0126 135176.6 29731.7483 196826.1 34929.1963 243096.3 37532.066 265444.5 43867.2776 325060.5 48387.8929 365279.5 51687.2146 405986.3 58611.4662 470388.7

TE D

Pr 13.78509 13.8103 15.48003 14.88776 15.0009 14.54944 14.89987 13.57908 14.12815

EP

Vel 0.767586 1.304545 1.853157 2.307685 2.51621 3.101358 3.467357 3.935347 4.516705

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

0.3% 50nm0.3% 50nm0.3% 50nm 1.07283 1.088895 1.189802 1.197519 1.220186 1.331312 1.092166 1.195376 1.190429 1.155977 1.234428 1.268291 1.071911 1.150286 1.174704 1.167418 1.228876 1.28602 1.112423 1.188638 1.22045 1.157526 1.167722 1.291397 1.108565 1.145661 1.227452

ACCEPTED MANUSCRIPT

Nu_Gen 52.01392 109.5255 126.9408 149.2917 161.4681 182.3632 209.2581 236.2014 272.1572

(Hnf/Hpf)V 1.370130052 1.296301535 1.283756653 1.324405837 1.289846457 1.346430765 1.318479734 1.353072011 1.340044821

(Hnf/Hpf)Re 1.537441677 1.513339277 1.592212691 1.582594713 1.55742004 1.551848589 1.543975997 1.500626002 1.532098163

(Hnf/Hpf)Pe0.5% 13nm 1.599731 1.489318 1.447077 1.5095 1.465359 1.554578 1.51327 1.589468 1.552256

RI PT

Nu_exp-0.5sNu_DB 79.47883 64.97121 142.8185 119.4484 168.6683 136.156 193.8406 155.8581 203.7651 166.9166 227.138 184.7466 254.3888 208.6477 276.3672 231.0418 319.2169 262.5832

SC

h_exp-0.5s K 1389.448 0.134611 2445.348 0.13184 2818.264 0.128659 3284.955 0.130489 3438.53 0.129937 3912.965 0.13265 4349.012 0.131639 4865.766 0.135567 5521.925 0.133197

M AN U

Re^0.8 Pr^0.4 Pe 14144.63 78838.83 27114.33 174758.2 32807.68 216325.8 36219.19 248522.8 39187.97 273075.1 41381.97 298100.7 47507.67 351834.9 49632.14 380732.8 58319.86 459362

TE D

Pr 14.65539 15.71246 17.3558 16.33912 16.62016 15.36753 15.79295 14.33289 15.15173

EP

Vel 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418

AC C

RE 5379.509 11122.27 12464.18 15210.3 16430.35 19398.08 22277.97 26563.57 30317.47

1.058302489 1.099738065 1.108348345 1.135471921 1.101384653 1.176735755 1.143075549 1.138414644 1.156510411

0.5% 13nm0.5% 13nm 1.187536 1.235649 1.283865 1.263487 1.374658 1.249353 1.356829 1.294162 1.329863 1.251252 1.356264 1.358649 1.338573 1.311951 1.26256 1.337308 1.32226 1.339657

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

RE Vel Pr Re^0.8 Pr^0.4 Pe h_exp-0.5l K Nu_exp-0.5lNu_DB Nu_Gen (Hnf/Hpf)V (Hnf/Hpf)Re (Hnf/Hpf)Pe0.5% 50nm 4922.87805 0.699653673 14.59087644 13117.66821 71829.10536 1284.608568 0.128112 77.2099 60.41373 47.33686322 1.422590845 1.525969862 1.593409 9750.402834 1.369898174 14.33141543 22259.076 139737.0737 2046.873625 0.128373 122.7747 103.6243 93.08967541 1.324207643 1.407418926 1.490866 13180.32319 2.081466016 16.62645037 32865.51092 219141.9895 2971.416699 0.124479 183.8058 139.955 131.5091157 1.375573466 1.605362507 1.51001 18148.94292 2.845290758 16.48304217 42084.13815 299149.7916 3849.468936 0.124687 237.7217 180.1457 176.4150658 1.387762624 1.610164159 1.525059 20828.32383 3.363085294 17.08011992 48687.1522 355750.2688 4210.704877 0.123891 261.7002 204.0082 203.0491413 1.327945304 1.577544977 1.45223 24946.99404 3.911925305 16.48847461 54299.40348 411337.8779 5065.259953 0.124683 312.8139 232.3885 235.9882169 1.415484068 1.64262173 1.555391 29650.52862 4.804751989 17.15686942 64873.00241 508710.2476 5982.985833 0.123804 372.1111 271.0997 280.3462331 1.418393995 1.689827704 1.550024

0.5% 50nm 1.120787317 1.123796049 1.18396894 1.210760282 1.123654624 1.237425533 1.230750039

1.202234411 1.194413758 1.381750515 1.404795588 1.334855963 1.43599078 1.466274899

0.5% 50nm 1.255366 1.265231 1.29968 1.330545 1.228819 1.359733 1.344966

ACCEPTED MANUSCRIPT

1.8

0.5% 50nm 1.7

RI PT

0.5% 13nm 1.6

0.3% 50nm 0.3% 13nm

SC

1.4 1.3

0.2% 50nm

M AN U

hnf / hbf

1.5

1.2 1.1

0.9

AC C

EP

0

TE D

1

2

4

u (m/s)

0.2% 13nm 0.05% 50nm 0.05% 13nm 6

8

ACCEPTED MANUSCRIPT

0.80 1.29 1.80 2.23 2.66 3.07 3.42 3.97 4.58 Vel 0.70 1.26 1.56 2.31 2.75 3.18 3.28 4.03 4.73

H 329.594 679.478 1183.04 1636.336 2059.792 2462.359 2849.026 3222.952 3586.306 3940.664 4287.216 4626.894 4960.442 5288.47 5611.485 5929.914 6244.122 888.0548 1536.526 1841.624 2463.771 2424.544 2806.421 3320.008 3641.717 4097.511 #VALUE! 888.0548 1447.366 1894.37 2244.16 2586.982 2904.682 3165.46 3561.468 3994.658 #VALUE! 891.291 1425.054 1690.124 2312.586 2655.211 2981.576 3059.105 3605.963 4104.4

RI PT

Nu 24.17023 50.30751 87.59046 121.1518 152.5038 182.3093 210.9375 238.6224 265.5246 291.7607 317.4189 342.5681 367.2635 391.5502 415.4657 439.0417 462.3052 65.75021 113.762 136.351 182.4138 179.5095 207.7831 245.8083 269.6272 303.3734 #VALUE! 65.75021 107.1607 140.2562 166.1542 191.5361 215.0582 234.3658 263.6856 295.7584 #VALUE! 65.98982 105.5088 125.1342 171.2203 196.5877 220.7513 226.4915 266.9799 303.8835

SC

Pe 23304.19 58260.47 116520.9 174781.4 233041.9 291302.3 349562.8 407823.3 466083.8 524344.2 582604.7 640865.2 699125.6 757386.1 815646.6 873907 932167.5 81415 161558.4 202607.8 291511.2 285721 343040.8 423232.1 475102.7 550560.2 #VALUE! 81415 149926.2 209887.1 259401.3 309846.4 358119.5 398750 462052.1 533340.2 #VALUE! 81786.03 147042.8 181992.3 269325.2 320094.7 370008.8 382074.3 469279.1 551717.6

M AN U

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

TE D

Vel

Re Pr 1536.202 3840.506 7681.011 11521.52 15362.02 19202.53 23043.03 26883.54 30724.04 34564.55 38405.06 42245.56 46086.07 49926.57 53767.08 57607.58 61448.09 5366.843 10649.86 13355.82 19216.29 18834.61 22613.1 27899.28 31318.57 36292.7 #VALUE! 5366.843 9883.071 13835.67 17099.62 20424.94 23607.08 26285.43 30458.28 35157.56 #VALUE! 5391.301 9692.999 11996.86 17753.8 21100.51 24390.82 25186.17 30934.68 36368.99

EP

0.20 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 0.70 1.39 1.74 2.50 2.45 2.94 3.63 4.08 4.72

AC C

V

#VALUE! 948.068 1494.933 1849.591 2302.415 2485.954 2743.895 2933.17 3570.648 3966.328 #VALUE! 808.6815 1441.913 1677.676 2131.788 2409.405 2731.215 3182.288 3675.899 4093.567 #VALUE! 880.739 1401.932 1848.404 2204.555 2460.67 2780.331 3225.505 3697.252 4162.99 939.1149 1287.928 1706.285 2032.511 2382.44 2922.599 3348.653 3729.974 4048.468 957.4169 1463.412 1937.89 2309.62 2475.124 2925.775 3198.882 3539.858

SC

#VALUE! 70.1935 110.6826 136.9409 170.4673 184.0562 203.1538 217.1674 264.3653 293.6608 #VALUE! 59.87353 106.7571 124.2126 157.8343 178.3886 202.215 235.6117 272.1579 303.0814 #VALUE! 65.20856 103.7969 136.853 163.2219 182.1842 205.8514 238.8114 273.7388 308.2214 69.53063 95.35623 126.3307 150.484 176.3922 216.3847 247.9291 276.1615 299.7424 70.88568 108.3488 143.4784 171.0007 183.2544 216.6199 236.8403 262.0856

M AN U

#VALUE! 88349.5 156110.4 203703.9 267845.4 294795.7 333514.1 362515.3 463541.5 528616.3 #VALUE! 72423.01 149220.6 180318.3 243267.8 283492.8 331588.7 401401.6 480683.5 549897.9 #VALUE! 80577.5 144066.6 203540.6 253691.5 291052.6 339059 408227.1 484176.3 561579.8 87307.82 129574.4 184170.1 229190.1 279532.4 360882.9 427801.6 489538.7 542335.7 89439.86 152006.8 215931.6 268893.6 293191.2 361373.2 404019.7 458550.3

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

#VALUE! 5823.962 10290.73 13428.08 17656.26 19432.81 21985.11 23896.86 30556.46 34846.16 #VALUE! 4774.094 9836.557 11886.51 16036.11 18687.72 21858.18 26460.23 31686.46 36249.04 #VALUE! 5311.635 9496.808 13417.31 16723.24 19186.06 22350.63 26910.16 31916.7 37019.1 5755.295 8541.493 12140.41 15108.11 18426.66 23789.25 28200.5 32270.18 35750.54 5895.838 10020.23 14234.12 17725.35 19327.04 23821.57 26632.81 30227.45

AC C

Vel 0.758229 1.339763 1.748217 2.298689 2.52998 2.862267 3.11116 3.978182 4.536663 Vel 0.62 1.28 1.55 2.09 2.43 2.85 3.44 4.13 4.72 Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561 0.75 1.11 1.58 1.97 2.40 3.10 3.67 4.20 4.65 0.77 1.30 1.85 2.31 2.52 3.10 3.47 3.94

RI PT

ACCEPTED MANUSCRIPT

3952.363 998.3795 1857.162 2161.295 2441.875 2624.52 2861.127 3247.374 3540.343 4056.825 889.0085 1521.774 2126.644 2730.868 3121.689 3522.993 4152.754 922.0801 1565.064 1679.369 2249.668 2227.969 2716.355 3066.233 3597.444 4107.391 1048.957 1534.846 1779.974 2223.705 2342.924 2874.383 3095.506 3686.68 3988.522 914.2035 1454.451 1555.335 2199.68 2436.893 2900.474 2917.17 3607.21 3976.339 1004.491 1568.337 1752.876

SC

292.6269 73.91849 137.5014 160.0189 180.7927 194.3154 211.8334 240.4306 262.1216 300.3611 65.82082 112.6698 157.4535 202.1893 231.1251 260.837 307.4635 68.26939 115.875 124.3379 166.562 164.9554 201.1147 227.0192 266.3492 304.1049 77.66317 113.6377 131.7865 164.6397 173.4665 212.8149 229.1865 272.9561 295.304 67.68622 107.6853 115.1546 162.8609 180.4238 214.7467 215.9827 267.0723 294.402 74.371 116.1173 129.7803

M AN U

526290.7 94248.47 204746.7 247484.1 288276.4 315476.6 351419.7 411689.8 458628.9 543735.4 81524.3 159621.8 242534.4 331535.9 391869.9 455821.2 559854.2 85332.71 165317.9 180545.8 260197.3 257064 329335 383187.4 467893.8 552220.2 100254 161337.7 194165.4 256449.1 273749 353456.2 387765.5 482446.4 532316.2 84422.53 150844.2 164034.4 252990.5 287541.3 357471.2 360045 469482.1 530284.5 94970.23 165750.2 190477.5

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

34692.86 6212.82 13496.81 16314.04 19003.06 20796.08 23165.44 27138.42 30232.63 35842.8 5374.048 10522.2 15987.76 21854.71 25831.9 30047.54 36905.35 5625.096 10897.69 11901.5 17152.1 16945.55 21709.62 25259.55 30843.37 36402.12 6608.704 10635.31 12799.3 16905.02 18045.42 23299.68 25561.34 31802.66 35090.06 5565.097 9943.588 10813.08 16677.03 18954.6 23564.35 23734.02 30948.06 34956.13 6260.398 10926.18 12556.2

AC C

4.52 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418 0.70 1.37 2.08 2.85 3.36 3.91 4.80

RI PT

ACCEPTED MANUSCRIPT

SC

2257.352 2365.024 2768.268 2927.392 3553.058 3961.52 803.2339 1420.566 1499.242 1965.644 2151.631 2579.476 2883.869 3438.884 3743.633 902.7711 1428.844 1703.752 2108.964 2296.182 2705.142 3015.379 3662.634 3992.714 885.5582 1219.384 1485.108 1828.159 2069.969 2588.067 2903.419 3362.635 3600.096 937.577 1421.87 1731.072 2127.646 2306.481 2735.096 2961.279 3457.199 3769.163 898.955 1552.341 1696.466 2012.643 2106.711

M AN U

167.1308 175.1027 204.9583 216.7396 263.0629 293.3049 59.4702 105.1765 111.0015 145.5332 159.3034 190.9804 213.5173 254.6097 277.1729 66.83978 105.7894 126.1432 156.1444 170.0058 200.2846 223.254 271.1758 295.6144 65.56537 90.28131 109.9551 135.3541 153.2573 191.6165 214.9647 248.9643 266.5456 69.41676 105.2731 128.1659 157.5277 170.7683 202.5023 219.2485 255.9657 279.063 66.55724 114.9329 125.6037 149.013 155.9776

TE D

261308.6 276980.4 337221.2 361622.8 460688.7 527815.4 71813.69 146464.2 156673 219804.1 246101.6 308723.1 354914.9 442259 491780.6 83104.93 147531.8 183828.5 240016.5 266939.4 327636.5 375259.8 478516.1 533015.7 81129 121012.5 154829 200757.6 234482 310008.9 357924.9 430035.5 468325 87129.13 146632.3 187520.5 242677.2 268436.8 332177.6 366862.9 445205.2 495976.2 82666.04 163639.6 182846.3 226393.1 239696.1

EP

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

AC C

17225.35 18258.43 22229.48 23838.02 30368.41 34793.37 4733.928 9654.858 10327.82 14489.39 16222.91 20350.89 23395.84 29153.53 32417.97 5478.242 9725.234 12117.9 15821.79 17596.53 21597.66 24736.97 31543.58 35136.17 5347.989 7977.094 10206.26 13233.86 15456.95 20435.66 23594.26 28347.76 30871.78 5743.516 9665.941 12361.27 15997.18 17695.24 21897.01 24183.45 29347.74 32694.54 5449.311 10787.06 12053.15 14923.74 15800.66

RI PT

ACCEPTED MANUSCRIPT

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

286166.1 327696.2 388219.8 452039.2 74314.91 142951.1 197652.6 268687.9 310975.8 374645.1 448248.3

179.7332 200.3137 229.4012 259.1042 61.12155 103.1534 133.6767 170.8961 192.0945 222.9614 257.3645

2427.565 2705.536 3098.406 3499.589 825.5378 1393.241 1805.503 2308.206 2594.523 3011.427 3476.091

AC C

EP

TE D

M AN U

SC

18863.95 21601.59 25591.28 29798.23 4898.807 9423.274 13029.18 17711.79 20499.4 24696.45 29548.34

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

Re

RePR 15.9 14473.49 15.9 76391.51

RI PT

M AN U TE D EP AC C

Pr 5000 40000

SC

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04601731 73.228819 60.5341941 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8333743 114.02112 103.854921 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6091968 145.27525 136.771494 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5438912 184.39553 180.878658 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9080838 216.74782 216.986307 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1383667 241.10514 246.006532 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2960579 247.95851 253.655111 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575419 277.97486 290.119402 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7894632 294.97439 309.411637 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718015 4523.427 42245.56 5.5 15.9 671704.4 0.105

0 550000

0 40000

0 5

1 1

ACCEPTED MANUSCRIPT

Nu_DB 65.30587 111.9013 130.5425 175.1432 172.3848 201.7167 234.2418 264.4811 297.8724

Nu_Gen 52.65631 101.9563 121.436 171.1343 168.0321 201.7188 238.1897 274.8055 314.1761

(Hnf/Hpf)V 1.10476451 1.07797523 1.01117157 1.0026325 1.0162503 1.05518168 1.04139384 1.07324153 1.08373015

M AN U TE D EP

(Hnf/Hpf)Re 1.075865026 1.076560447 1.082089197 1.065081018 1.079320978 1.090168255 1.127583933 1.08016342 1.087367899

RI PT

h_exp-0.05sK Nu_exp-0.05s 996.5051 0.117904 65.07888109 1682.359 0.117007 110.7126768 1891.455 0.114796 126.870515 2509.066 0.115016 167.9756577 2502.653 0.115023 167.5351509 3007.808 0.115881 199.861825 3511.754 0.114451 236.2631742 3969.847 0.116747 261.8304753 4510.361 0.116847 297.2255786

SC

Vel Pr Re^0.8 Pr^0.4 Pe 0.698716 13.9586495 13807.9887 77437.65 1.386518 14.5095547 24215.8436 154778.6 1.73881 16.1181284 30089.3486 197782.3 2.501792 15.937742 40097.8984 283984.9 2.4521 15.9363724 39464.3398 278393.2 2.944027 15.2837703 45035.2234 331804.9 3.632241 16.4055232 54567.068 414396.2 4.077402 14.6907251 57662.4105 456410 4.72499 14.6135602 64737.5239 528148.6

AC C

RE 5547.646 10667.36 12270.8 17818.39 17469.05 21709.62 25259.55 31067.9 36140.99

(Hnf/Hpf)Pe 1.16385706 1.129098234 1.043345026 1.036233883 1.050160357 1.096795616 1.071947184 1.121686405 1.133935255

0.05% 13nm0.05% 13nm0.05% 13nm 1.083228 1.054891 1.141168 1.030881 1.029528 1.079771 0.979 1.047661 1.01015 0.998521 1.060714 1.031985 0.992135 1.053709 1.02524 1.015733 1.049411 1.055791 1.017159 1.101343 1.047001 1.0871 1.094111 1.136171 1.091849 1.095514 1.14243

ACCEPTED MANUSCRIPT

K 0.111858 0.112378 0.110702 0.111413 0.1102 0.111389 0.111076 0.112173 0.111341

Nu_exp-0.5lNu_DB 75.93648 74.21862 112.1558 109.9809 140.3751 138.304 168.7731 166.8019 185.5256 186.3786 224.8539 215.7783 246.1604 233.3266 276.9776 269.4173 316.0861 296.4203

Nu_Gen 61.61831 100.0557 129.9734 162.225 183.2382 217.8415 237.7497 280.8886 311.7457

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe0.05% 50nm0.05% 50nm0.05% 50nm 1.099152 1.099152 1.11 1.05866 1.05866 1.069107784 1.113433 1.113433 1.128392 1.050546 1.050546 1.064659623 1.048862 1.048862 1.050909 1.013903 1.013903 1.015881482 1.071331 1.071331 1.078583 1.042452 1.042452 1.04950811 1.010491 1.010491 1.008793 1.001131 1.001131 0.999448778 1.102514 1.102514 1.109732 1.09573 1.09573 1.102903575 1.104432 1.104432 1.109397 1.126202 1.126202 1.131265382 1.115429 1.115429 1.128802 1.059624 1.059624 1.072328062 1.126469 1.126469 1.133281 1.095379 1.095379 1.102003867

RI PT

h_exp-05l 1103.125 1636.863 2018.149 2442.011 2655.192 3252.765 3550.96 4034.975 4570.553

M AN U

SC

Re^0.8 Pr^0.4 Pe 16196.9517 93294.23935 23464.2506 149681.3739 31871.4236 212550.6416 37151.5957 261122.9317 44053.3846 315206.0235 48115.4826 360595.7866 52801.0675 402532.3488 57990.7295 462121.5199 66256.6455 537361.1463

TE D

Pr 14.71455 14.16976 16.1123 15.22325 16.80809 15.25252 15.63185 14.3803 15.31377

EP

Vel 0.798449 1.286689 1.801282 2.22622 2.659148 3.073434 3.422132 3.9654 4.577204

AC C

RE 6340.269 10563.44 13191.82 17152.91 18753.23 23641.72 25750.78 32135.73 35090.06

ACCEPTED MANUSCRIPT

Nu_exp-0.2sNu_DB 61.4864 56.11831 101.3997 99.65 117.0625 113.4808 144.1866 145.8541 165.7678 163.2296 190.284 187.2735 221.3851 216.3877 265.5391 251.2614 288.2756 278.3376

Nu_Gen 43.53593 89.28494 103.3352 139.4522 158.355 186.1855 218.9646 259.7459 291.0525

(Hnf/Hpf)V 1.275443102 1.170830127 1.122631027 1.106681242 1.109358997 1.144029489 1.127668695 1.180545902 1.141684605

(Hnf/Hpf)Re 1.284093219 1.194488999 1.227873383 1.167623135 1.207360834 1.198318539 1.213244673 1.248157954 1.227576581

RI PT

h_exp-0.2s K 1047.632 0.131196 1714.759 0.130214 1913.001 0.125831 2396.274 0.127968 2714.888 0.126108 3173.68 0.128426 3644.946 0.126775 4407.746 0.127814 4746.987 0.126795

M AN U

SC

Re^0.8 Pr^0.4 Pe 11433.4124 62118.39 20582.3174 128792.6 25193.9201 160907.9 31208.9145 213539.6 36054.3463 252393.2 39768.2765 290018.6 47238.9297 355530.6 53855.0394 422040.8 60702.7119 486622

TE D

Pr 13.12195 13.42481 15.1415 14.239 15.01334 14.05985 14.72286 14.27954 14.69851

EP

Vel 0.621545 1.280633 1.547519 2.087761 2.432977 2.845743 3.444888 4.125298 4.719306

AC C

RE 4733.928 9593.626 10626.95 14996.81 16811.26 20627.44 24148.21 29555.64 33106.89

(Hnf/Hpf)Pe0.2% 13nm0.2% 13nm0.2% 13nm 1.459534 1.201224 1.20937 1.374602 1.333129 1.070038 1.09166 1.218366 1.244615 1.003994 1.098114 1.113087 1.243185 0.99789 1.052841 1.120974 1.232173 0.999596 1.087901 1.110258 1.288856 1.030742 1.079656 1.161228 1.257683 1.033747 1.112196 1.152933 1.325912 1.10662 1.169998 1.242883 1.274226 1.039619 1.117833 1.160312

ACCEPTED MANUSCRIPT

K 0.125829 0.125479 0.121532 0.123265 0.122087 0.123829 0.122335 0.124765 0.123391

Nu_exp-0.2lNu_DB 66.72749 62.98494 111.4692 100.0137 138.1021 128.3917 167.2666 155.0902 186.1079 171.6368 216.0257 196.3328 243.429 224.3843 286.1464 262.6416 310.7312 293.1144

Nu_Gen 50.56447 89.71656 119.5899 149.7068 167.8881 196.5216 228.0024 273.6766 308.9321

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.218923 1.195139 1.348647044 1.27567 1.25802 1.410155626 1.161001 1.237999 1.252011073 1.195828 1.22944 1.303905023 1.180646 1.243792 1.277970146 1.230182 1.250703 1.346278479 1.180497 1.248452 1.279710732 1.234643 1.233206 1.359003846 1.177607 1.207667 1.285088932

RI PT

h_exp-0.2l 1090.419 1816.499 2179.715 2677.686 2950.823 3474.048 3867.521 4636.501 4979.387

SC

Re^0.8 Pr^0.4 Pe 12902.1264 72085.25 20590.1435 129029.1 28553.2441 188025.5 33282.4345 231137 37719.4422 267611.9 41666.9541 307506 49399.4289 374652.4 54765.8073 435952.8 62745.437 511129.2

M AN U

13.241 13.352 15.18486 14.30861 14.8869 14.04574 14.93123 13.63922 14.24912

TE D

Pr

EP

Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561

AC C

RE 5444.095 9663.65 12382.43 16153.7 17976.33 21893.18 25091.86 31963.17 35870.93

0.2% 50nm0.2% 50nm0.2% 50nm 1.176226 1.153275 1.301406 1.193207 1.176698 1.318999 1.072299 1.143413 1.156355 1.109216 1.140394 1.209465 1.072065 1.129403 1.160439 1.117188 1.135824 1.222621 1.099887 1.163201 1.192325 1.151444 1.150105 1.267425 1.096179 1.12416 1.196228

ACCEPTED MANUSCRIPT

Nu_exp-0.3sNu_DB 67.6355 64.03218 102.797 88.42092 126.7817 114.3404 156.1554 137.6449 174.9715 159.5505 222.3501 196.6073 248.0932 223.3202 286.7741 251.8322 314.4038 271.8178

Nu_Gen 51.22818 77.12423 104.0727 130.0495 153.8867 195.9333 226.02 259.8369 282.7461

(Hnf/Hpf)V 1.185641083 1.329027593 1.195267188 1.252527278 1.180590009 1.229592283 1.185193237 1.248724405 1.252069608

M AN U TE D

(Hnf/Hpf)Re 1.254279776 1.374293179 1.332620188 1.353085775 1.31848137 1.355397074 1.340037919 1.359803446 1.388479936

RI PT

h_exp-0.3s K 1130.946 0.128753 1738.584 0.130228 2071.507 0.125812 2585.771 0.127504 2856.874 0.125723 3650.063 0.126402 4031.153 0.125114 4730.886 0.127026 5148.601 0.126093

SC

Pr Re^0.8 Pr^0.4 Pe 14.21163 13685.3757 76235.97 13.65727 18452.0874 111870.6 15.51732 25760.9561 164436.5 14.7233 30049.3645 201972.8 15.55859 36004.1494 249717 15.22936 43800.6874 320760.4 15.87839 51013.3747 384063.8 14.90663 55387.4257 432433.3 15.38466 60926.0106 483316.3

EP

Vel 0.749289 1.112027 1.580575 1.966943 2.398989 3.09715 3.671456 4.201294 4.654405

AC C

RE 5364.338 8191.285 10596.97 13717.9 16050.11 21061.97 24187.83 29009.45 31415.48

(Hnf/Hpf)Pe 1.337506581 1.51288134 1.324554106 1.402612492 1.307718957 1.367532613 1.307640674 1.395690271 1.389587622

0.3% 13nm 0.3% 13nm 0.3% 13nm 1.048587 1.109291 1.182897 1.16447 1.204131 1.32556 1.050256 1.170945 1.163857 1.086559 1.173792 1.216757 1.031577 1.152064 1.14266 1.079922 1.190414 1.201072 1.029352 1.163836 1.135699 1.089969 1.186926 1.218251 1.123628 1.246045 1.247039

ACCEPTED MANUSCRIPT

K 0.102582 0.126427 0.123222 0.124255 0.124042 0.124885 0.124227 0.126915 0.125735

Nu_exp-0.3lNu_DB 85.99118 67.21606 120.1099 102.416 150.6336 132.1555 188.1594 158.9348 188.3668 170.0043 239.7737 202.3768 255.5954 220.067 284.4845 248.5357 312.3335 275.2068

Nu_Gen 54.71687 92.06135 123.5585 153.6267 165.9727 203.0339 223.0541 257.2314 287.9402

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.178051 1.195691 1.306495845 1.32676 1.351873 1.474992721 1.224673 1.340405 1.334858122 1.294313 1.382152 1.420067544 1.207024 1.295278 1.322774477 1.308613 1.377506 1.441560308 1.269144 1.356096 1.392390322 1.304148 1.315634 1.454974513 1.270445 1.312958 1.406691714

RI PT

h_exp-0.3l 1145.606 1972.101 2410.568 3036.336 3034.471 3888.86 4123.626 4689.025 5100.145

M AN U

SC

Re^0.8 Pr^0.4 Pe 14105.5796 79778.58 21516.0126 135176.6 29731.7483 196826.1 34929.1963 243096.3 37532.066 265444.5 43867.2776 325060.5 48387.8929 365279.5 51687.2146 405986.3 58611.4662 470388.7

TE D

Pr 13.78509 13.8103 15.48003 14.88776 15.0009 14.54944 14.89987 13.57908 14.12815

EP

Vel 0.767586 1.304545 1.853157 2.307685 2.51621 3.101358 3.467357 3.935347 4.516705

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

0.3% 50nm0.3% 50nm0.3% 50nm 1.07283 1.088895 1.189802 1.197519 1.220186 1.331312 1.092166 1.195376 1.190429 1.155977 1.234428 1.268291 1.071911 1.150286 1.174704 1.167418 1.228876 1.28602 1.112423 1.188638 1.22045 1.157526 1.167722 1.291397 1.108565 1.145661 1.227452

ACCEPTED MANUSCRIPT

Nu_Gen 52.01392 109.5255 126.9408 149.2917 161.4681 182.3632 209.2581 236.2014 272.1572

(Hnf/Hpf)V 1.370130052 1.296301535 1.283756653 1.324405837 1.289846457 1.346430765 1.318479734 1.353072011 1.340044821

(Hnf/Hpf)Re 1.537441677 1.513339277 1.592212691 1.582594713 1.55742004 1.551848589 1.543975997 1.500626002 1.532098163

(Hnf/Hpf)Pe0.5% 13nm 1.599731 1.489318 1.447077 1.5095 1.465359 1.554578 1.51327 1.589468 1.552256

RI PT

Nu_exp-0.5sNu_DB 79.47883 64.97121 142.8185 119.4484 168.6683 136.156 193.8406 155.8581 203.7651 166.9166 227.138 184.7466 254.3888 208.6477 276.3672 231.0418 319.2169 262.5832

SC

h_exp-0.5s K 1389.448 0.134611 2445.348 0.13184 2818.264 0.128659 3284.955 0.130489 3438.53 0.129937 3912.965 0.13265 4349.012 0.131639 4865.766 0.135567 5521.925 0.133197

M AN U

Re^0.8 Pr^0.4 Pe 14144.63 78838.83 27114.33 174758.2 32807.68 216325.8 36219.19 248522.8 39187.97 273075.1 41381.97 298100.7 47507.67 351834.9 49632.14 380732.8 58319.86 459362

TE D

Pr 14.65539 15.71246 17.3558 16.33912 16.62016 15.36753 15.79295 14.33289 15.15173

EP

Vel 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418

AC C

RE 5379.509 11122.27 12464.18 15210.3 16430.35 19398.08 22277.97 26563.57 30317.47

1.058302489 1.099738065 1.108348345 1.135471921 1.101384653 1.176735755 1.143075549 1.138414644 1.156510411

0.5% 13nm0.5% 13nm 1.187536 1.235649 1.283865 1.263487 1.374658 1.249353 1.356829 1.294162 1.329863 1.251252 1.356264 1.358649 1.338573 1.311951 1.26256 1.337308 1.32226 1.339657

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

RE Vel Pr Re^0.8 Pr^0.4 Pe h_exp-0.5l K Nu_exp-0.5lNu_DB Nu_Gen (Hnf/Hpf)V (Hnf/Hpf)Re (Hnf/Hpf)Pe0.5% 50nm 4922.87805 0.699653673 14.59087644 13117.66821 71829.10536 1284.608568 0.128112 77.2099 60.41373 47.33686322 1.422590845 1.525969862 1.593409 9750.402834 1.369898174 14.33141543 22259.076 139737.0737 2046.873625 0.128373 122.7747 103.6243 93.08967541 1.324207643 1.407418926 1.490866 13180.32319 2.081466016 16.62645037 32865.51092 219141.9895 2971.416699 0.124479 183.8058 139.955 131.5091157 1.375573466 1.605362507 1.51001 18148.94292 2.845290758 16.48304217 42084.13815 299149.7916 3849.468936 0.124687 237.7217 180.1457 176.4150658 1.387762624 1.610164159 1.525059 20828.32383 3.363085294 17.08011992 48687.1522 355750.2688 4210.704877 0.123891 261.7002 204.0082 203.0491413 1.327945304 1.577544977 1.45223 24946.99404 3.911925305 16.48847461 54299.40348 411337.8779 5065.259953 0.124683 312.8139 232.3885 235.9882169 1.415484068 1.64262173 1.555391 29650.52862 4.804751989 17.15686942 64873.00241 508710.2476 5982.985833 0.123804 372.1111 271.0997 280.3462331 1.418393995 1.689827704 1.550024

0.5% 50nm 1.120787317 1.123796049 1.18396894 1.210760282 1.123654624 1.237425533 1.230750039

1.202234411 1.194413758 1.381750515 1.404795588 1.334855963 1.43599078 1.466274899

0.5% 50nm 1.255366 1.265231 1.29968 1.330545 1.228819 1.359733 1.344966

ACCEPTED MANUSCRIPT

1.8

0.5% 50nm 1.7

RI PT

0.5% 13nm 1.6

0.3% 50nm 0.3% 13nm

SC

1.4 1.3

M AN U

hnf / hbf

1.5

1.2 1.1

0.9

AC C

EP

0

TE D

1

200000

400000

Pe

0.2% 50nm 0.2% 13nm 0.05% 50nm 0.05% 13nm 600000

800000

ACCEPTED MANUSCRIPT

0.80 1.29 1.80 2.23 2.66 3.07 3.42 3.97 4.58 Vel 0.70 1.26 1.56 2.31 2.75 3.18 3.28 4.03 4.73

H 329.594 679.478 1183.04 1636.336 2059.792 2462.359 2849.026 3222.952 3586.306 3940.664 4287.216 4626.894 4960.442 5288.47 5611.485 5929.914 6244.122 888.0548 1536.526 1841.624 2463.771 2424.544 2806.421 3320.008 3641.717 4097.511 #VALUE! 888.0548 1447.366 1894.37 2244.16 2586.982 2904.682 3165.46 3561.468 3994.658 #VALUE! 891.291 1425.054 1690.124 2312.586 2655.211 2981.576 3059.105 3605.963 4104.4

RI PT

Nu 24.17023 50.30751 87.59046 121.1518 152.5038 182.3093 210.9375 238.6224 265.5246 291.7607 317.4189 342.5681 367.2635 391.5502 415.4657 439.0417 462.3052 65.75021 113.762 136.351 182.4138 179.5095 207.7831 245.8083 269.6272 303.3734 #VALUE! 65.75021 107.1607 140.2562 166.1542 191.5361 215.0582 234.3658 263.6856 295.7584 #VALUE! 65.98982 105.5088 125.1342 171.2203 196.5877 220.7513 226.4915 266.9799 303.8835

SC

Pe 23304.19 58260.47 116520.9 174781.4 233041.9 291302.3 349562.8 407823.3 466083.8 524344.2 582604.7 640865.2 699125.6 757386.1 815646.6 873907 932167.5 81415 161558.4 202607.8 291511.2 285721 343040.8 423232.1 475102.7 550560.2 #VALUE! 81415 149926.2 209887.1 259401.3 309846.4 358119.5 398750 462052.1 533340.2 #VALUE! 81786.03 147042.8 181992.3 269325.2 320094.7 370008.8 382074.3 469279.1 551717.6

M AN U

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

TE D

Vel

Re Pr 1536.202 3840.506 7681.011 11521.52 15362.02 19202.53 23043.03 26883.54 30724.04 34564.55 38405.06 42245.56 46086.07 49926.57 53767.08 57607.58 61448.09 5366.843 10649.86 13355.82 19216.29 18834.61 22613.1 27899.28 31318.57 36292.7 #VALUE! 5366.843 9883.071 13835.67 17099.62 20424.94 23607.08 26285.43 30458.28 35157.56 #VALUE! 5391.301 9692.999 11996.86 17753.8 21100.51 24390.82 25186.17 30934.68 36368.99

EP

0.20 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 0.70 1.39 1.74 2.50 2.45 2.94 3.63 4.08 4.72

AC C

V

#VALUE! 948.068 1494.933 1849.591 2302.415 2485.954 2743.895 2933.17 3570.648 3966.328 #VALUE! 808.6815 1441.913 1677.676 2131.788 2409.405 2731.215 3182.288 3675.899 4093.567 #VALUE! 880.739 1401.932 1848.404 2204.555 2460.67 2780.331 3225.505 3697.252 4162.99 939.1149 1287.928 1706.285 2032.511 2382.44 2922.599 3348.653 3729.974 4048.468 957.4169 1463.412 1937.89 2309.62 2475.124 2925.775 3198.882 3539.858

SC

#VALUE! 70.1935 110.6826 136.9409 170.4673 184.0562 203.1538 217.1674 264.3653 293.6608 #VALUE! 59.87353 106.7571 124.2126 157.8343 178.3886 202.215 235.6117 272.1579 303.0814 #VALUE! 65.20856 103.7969 136.853 163.2219 182.1842 205.8514 238.8114 273.7388 308.2214 69.53063 95.35623 126.3307 150.484 176.3922 216.3847 247.9291 276.1615 299.7424 70.88568 108.3488 143.4784 171.0007 183.2544 216.6199 236.8403 262.0856

M AN U

#VALUE! 88349.5 156110.4 203703.9 267845.4 294795.7 333514.1 362515.3 463541.5 528616.3 #VALUE! 72423.01 149220.6 180318.3 243267.8 283492.8 331588.7 401401.6 480683.5 549897.9 #VALUE! 80577.5 144066.6 203540.6 253691.5 291052.6 339059 408227.1 484176.3 561579.8 87307.82 129574.4 184170.1 229190.1 279532.4 360882.9 427801.6 489538.7 542335.7 89439.86 152006.8 215931.6 268893.6 293191.2 361373.2 404019.7 458550.3

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

#VALUE! 5823.962 10290.73 13428.08 17656.26 19432.81 21985.11 23896.86 30556.46 34846.16 #VALUE! 4774.094 9836.557 11886.51 16036.11 18687.72 21858.18 26460.23 31686.46 36249.04 #VALUE! 5311.635 9496.808 13417.31 16723.24 19186.06 22350.63 26910.16 31916.7 37019.1 5755.295 8541.493 12140.41 15108.11 18426.66 23789.25 28200.5 32270.18 35750.54 5895.838 10020.23 14234.12 17725.35 19327.04 23821.57 26632.81 30227.45

AC C

Vel 0.758229 1.339763 1.748217 2.298689 2.52998 2.862267 3.11116 3.978182 4.536663 Vel 0.62 1.28 1.55 2.09 2.43 2.85 3.44 4.13 4.72 Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561 0.75 1.11 1.58 1.97 2.40 3.10 3.67 4.20 4.65 0.77 1.30 1.85 2.31 2.52 3.10 3.47 3.94

RI PT

ACCEPTED MANUSCRIPT

3952.363 998.3795 1857.162 2161.295 2441.875 2624.52 2861.127 3247.374 3540.343 4056.825 889.0085 1521.774 2126.644 2730.868 3121.689 3522.993 4152.754 922.0801 1565.064 1679.369 2249.668 2227.969 2716.355 3066.233 3597.444 4107.391 1048.957 1534.846 1779.974 2223.705 2342.924 2874.383 3095.506 3686.68 3988.522 914.2035 1454.451 1555.335 2199.68 2436.893 2900.474 2917.17 3607.21 3976.339 1004.491 1568.337 1752.876

SC

292.6269 73.91849 137.5014 160.0189 180.7927 194.3154 211.8334 240.4306 262.1216 300.3611 65.82082 112.6698 157.4535 202.1893 231.1251 260.837 307.4635 68.26939 115.875 124.3379 166.562 164.9554 201.1147 227.0192 266.3492 304.1049 77.66317 113.6377 131.7865 164.6397 173.4665 212.8149 229.1865 272.9561 295.304 67.68622 107.6853 115.1546 162.8609 180.4238 214.7467 215.9827 267.0723 294.402 74.371 116.1173 129.7803

M AN U

526290.7 94248.47 204746.7 247484.1 288276.4 315476.6 351419.7 411689.8 458628.9 543735.4 81524.3 159621.8 242534.4 331535.9 391869.9 455821.2 559854.2 85332.71 165317.9 180545.8 260197.3 257064 329335 383187.4 467893.8 552220.2 100254 161337.7 194165.4 256449.1 273749 353456.2 387765.5 482446.4 532316.2 84422.53 150844.2 164034.4 252990.5 287541.3 357471.2 360045 469482.1 530284.5 94970.23 165750.2 190477.5

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

34692.86 6212.82 13496.81 16314.04 19003.06 20796.08 23165.44 27138.42 30232.63 35842.8 5374.048 10522.2 15987.76 21854.71 25831.9 30047.54 36905.35 5625.096 10897.69 11901.5 17152.1 16945.55 21709.62 25259.55 30843.37 36402.12 6608.704 10635.31 12799.3 16905.02 18045.42 23299.68 25561.34 31802.66 35090.06 5565.097 9943.588 10813.08 16677.03 18954.6 23564.35 23734.02 30948.06 34956.13 6260.398 10926.18 12556.2

AC C

4.52 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418 0.70 1.37 2.08 2.85 3.36 3.91 4.80

RI PT

ACCEPTED MANUSCRIPT

SC

2257.352 2365.024 2768.268 2927.392 3553.058 3961.52 803.2339 1420.566 1499.242 1965.644 2151.631 2579.476 2883.869 3438.884 3743.633 902.7711 1428.844 1703.752 2108.964 2296.182 2705.142 3015.379 3662.634 3992.714 885.5582 1219.384 1485.108 1828.159 2069.969 2588.067 2903.419 3362.635 3600.096 937.577 1421.87 1731.072 2127.646 2306.481 2735.096 2961.279 3457.199 3769.163 898.955 1552.341 1696.466 2012.643 2106.711

M AN U

167.1308 175.1027 204.9583 216.7396 263.0629 293.3049 59.4702 105.1765 111.0015 145.5332 159.3034 190.9804 213.5173 254.6097 277.1729 66.83978 105.7894 126.1432 156.1444 170.0058 200.2846 223.254 271.1758 295.6144 65.56537 90.28131 109.9551 135.3541 153.2573 191.6165 214.9647 248.9643 266.5456 69.41676 105.2731 128.1659 157.5277 170.7683 202.5023 219.2485 255.9657 279.063 66.55724 114.9329 125.6037 149.013 155.9776

TE D

261308.6 276980.4 337221.2 361622.8 460688.7 527815.4 71813.69 146464.2 156673 219804.1 246101.6 308723.1 354914.9 442259 491780.6 83104.93 147531.8 183828.5 240016.5 266939.4 327636.5 375259.8 478516.1 533015.7 81129 121012.5 154829 200757.6 234482 310008.9 357924.9 430035.5 468325 87129.13 146632.3 187520.5 242677.2 268436.8 332177.6 366862.9 445205.2 495976.2 82666.04 163639.6 182846.3 226393.1 239696.1

EP

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

AC C

17225.35 18258.43 22229.48 23838.02 30368.41 34793.37 4733.928 9654.858 10327.82 14489.39 16222.91 20350.89 23395.84 29153.53 32417.97 5478.242 9725.234 12117.9 15821.79 17596.53 21597.66 24736.97 31543.58 35136.17 5347.989 7977.094 10206.26 13233.86 15456.95 20435.66 23594.26 28347.76 30871.78 5743.516 9665.941 12361.27 15997.18 17695.24 21897.01 24183.45 29347.74 32694.54 5449.311 10787.06 12053.15 14923.74 15800.66

RI PT

ACCEPTED MANUSCRIPT

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

286166.1 327696.2 388219.8 452039.2 74314.91 142951.1 197652.6 268687.9 310975.8 374645.1 448248.3

179.7332 200.3137 229.4012 259.1042 61.12155 103.1534 133.6767 170.8961 192.0945 222.9614 257.3645

2427.565 2705.536 3098.406 3499.589 825.5378 1393.241 1805.503 2308.206 2594.523 3011.427 3476.091

AC C

EP

TE D

M AN U

SC

18863.95 21601.59 25591.28 29798.23 4898.807 9423.274 13029.18 17711.79 20499.4 24696.45 29548.34

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

Re

RePR 15.9 14473.49 15.9 76391.51

RI PT

M AN U TE D EP AC C

Pr 5000 40000

SC

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04601731 73.228819 60.5341941 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8333743 114.02112 103.854921 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6091968 145.27525 136.771494 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5438912 184.39553 180.878658 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9080838 216.74782 216.986307 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1383667 241.10514 246.006532 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2960579 247.95851 253.655111 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575419 277.97486 290.119402 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7894632 294.97439 309.411637 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718015 4523.427 42245.56 5.5 15.9 671704.4 0.105

0 550000

0 40000

0 5

1 1

ACCEPTED MANUSCRIPT

Nu_DB 65.30587 111.9013 130.5425 175.1432 172.3848 201.7167 234.2418 264.4811 297.8724

Nu_Gen 52.65631 101.9563 121.436 171.1343 168.0321 201.7188 238.1897 274.8055 314.1761

(Hnf/Hpf)V 1.10476451 1.07797523 1.01117157 1.0026325 1.0162503 1.05518168 1.04139384 1.07324153 1.08373015

M AN U TE D EP

(Hnf/Hpf)Re 1.075865026 1.076560447 1.082089197 1.065081018 1.079320978 1.090168255 1.127583933 1.08016342 1.087367899

RI PT

h_exp-0.05sK Nu_exp-0.05s 996.5051 0.117904 65.07888109 1682.359 0.117007 110.7126768 1891.455 0.114796 126.870515 2509.066 0.115016 167.9756577 2502.653 0.115023 167.5351509 3007.808 0.115881 199.861825 3511.754 0.114451 236.2631742 3969.847 0.116747 261.8304753 4510.361 0.116847 297.2255786

SC

Vel Pr Re^0.8 Pr^0.4 Pe 0.698716 13.9586495 13807.9887 77437.65 1.386518 14.5095547 24215.8436 154778.6 1.73881 16.1181284 30089.3486 197782.3 2.501792 15.937742 40097.8984 283984.9 2.4521 15.9363724 39464.3398 278393.2 2.944027 15.2837703 45035.2234 331804.9 3.632241 16.4055232 54567.068 414396.2 4.077402 14.6907251 57662.4105 456410 4.72499 14.6135602 64737.5239 528148.6

AC C

RE 5547.646 10667.36 12270.8 17818.39 17469.05 21709.62 25259.55 31067.9 36140.99

(Hnf/Hpf)Pe 1.16385706 1.129098234 1.043345026 1.036233883 1.050160357 1.096795616 1.071947184 1.121686405 1.133935255

0.05% 13nm0.05% 13nm0.05% 13nm 1.083228 1.054891 1.141168 1.030881 1.029528 1.079771 0.979 1.047661 1.01015 0.998521 1.060714 1.031985 0.992135 1.053709 1.02524 1.015733 1.049411 1.055791 1.017159 1.101343 1.047001 1.0871 1.094111 1.136171 1.091849 1.095514 1.14243

ACCEPTED MANUSCRIPT

K 0.111858 0.112378 0.110702 0.111413 0.1102 0.111389 0.111076 0.112173 0.111341

Nu_exp-0.5lNu_DB 75.93648 74.21862 112.1558 109.9809 140.3751 138.304 168.7731 166.8019 185.5256 186.3786 224.8539 215.7783 246.1604 233.3266 276.9776 269.4173 316.0861 296.4203

Nu_Gen 61.61831 100.0557 129.9734 162.225 183.2382 217.8415 237.7497 280.8886 311.7457

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe0.05% 50nm0.05% 50nm0.05% 50nm 1.099152 1.099152 1.11 1.05866 1.05866 1.069107784 1.113433 1.113433 1.128392 1.050546 1.050546 1.064659623 1.048862 1.048862 1.050909 1.013903 1.013903 1.015881482 1.071331 1.071331 1.078583 1.042452 1.042452 1.04950811 1.010491 1.010491 1.008793 1.001131 1.001131 0.999448778 1.102514 1.102514 1.109732 1.09573 1.09573 1.102903575 1.104432 1.104432 1.109397 1.126202 1.126202 1.131265382 1.115429 1.115429 1.128802 1.059624 1.059624 1.072328062 1.126469 1.126469 1.133281 1.095379 1.095379 1.102003867

RI PT

h_exp-05l 1103.125 1636.863 2018.149 2442.011 2655.192 3252.765 3550.96 4034.975 4570.553

M AN U

SC

Re^0.8 Pr^0.4 Pe 16196.9517 93294.23935 23464.2506 149681.3739 31871.4236 212550.6416 37151.5957 261122.9317 44053.3846 315206.0235 48115.4826 360595.7866 52801.0675 402532.3488 57990.7295 462121.5199 66256.6455 537361.1463

TE D

Pr 14.71455 14.16976 16.1123 15.22325 16.80809 15.25252 15.63185 14.3803 15.31377

EP

Vel 0.798449 1.286689 1.801282 2.22622 2.659148 3.073434 3.422132 3.9654 4.577204

AC C

RE 6340.269 10563.44 13191.82 17152.91 18753.23 23641.72 25750.78 32135.73 35090.06

ACCEPTED MANUSCRIPT

Nu_exp-0.2sNu_DB 61.4864 56.11831 101.3997 99.65 117.0625 113.4808 144.1866 145.8541 165.7678 163.2296 190.284 187.2735 221.3851 216.3877 265.5391 251.2614 288.2756 278.3376

Nu_Gen 43.53593 89.28494 103.3352 139.4522 158.355 186.1855 218.9646 259.7459 291.0525

(Hnf/Hpf)V 1.275443102 1.170830127 1.122631027 1.106681242 1.109358997 1.144029489 1.127668695 1.180545902 1.141684605

(Hnf/Hpf)Re 1.284093219 1.194488999 1.227873383 1.167623135 1.207360834 1.198318539 1.213244673 1.248157954 1.227576581

RI PT

h_exp-0.2s K 1047.632 0.131196 1714.759 0.130214 1913.001 0.125831 2396.274 0.127968 2714.888 0.126108 3173.68 0.128426 3644.946 0.126775 4407.746 0.127814 4746.987 0.126795

M AN U

SC

Re^0.8 Pr^0.4 Pe 11433.4124 62118.39 20582.3174 128792.6 25193.9201 160907.9 31208.9145 213539.6 36054.3463 252393.2 39768.2765 290018.6 47238.9297 355530.6 53855.0394 422040.8 60702.7119 486622

TE D

Pr 13.12195 13.42481 15.1415 14.239 15.01334 14.05985 14.72286 14.27954 14.69851

EP

Vel 0.621545 1.280633 1.547519 2.087761 2.432977 2.845743 3.444888 4.125298 4.719306

AC C

RE 4733.928 9593.626 10626.95 14996.81 16811.26 20627.44 24148.21 29555.64 33106.89

(Hnf/Hpf)Pe0.2% 13nm0.2% 13nm0.2% 13nm 1.459534 1.201224 1.20937 1.374602 1.333129 1.070038 1.09166 1.218366 1.244615 1.003994 1.098114 1.113087 1.243185 0.99789 1.052841 1.120974 1.232173 0.999596 1.087901 1.110258 1.288856 1.030742 1.079656 1.161228 1.257683 1.033747 1.112196 1.152933 1.325912 1.10662 1.169998 1.242883 1.274226 1.039619 1.117833 1.160312

ACCEPTED MANUSCRIPT

K 0.125829 0.125479 0.121532 0.123265 0.122087 0.123829 0.122335 0.124765 0.123391

Nu_exp-0.2lNu_DB 66.72749 62.98494 111.4692 100.0137 138.1021 128.3917 167.2666 155.0902 186.1079 171.6368 216.0257 196.3328 243.429 224.3843 286.1464 262.6416 310.7312 293.1144

Nu_Gen 50.56447 89.71656 119.5899 149.7068 167.8881 196.5216 228.0024 273.6766 308.9321

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.218923 1.195139 1.348647044 1.27567 1.25802 1.410155626 1.161001 1.237999 1.252011073 1.195828 1.22944 1.303905023 1.180646 1.243792 1.277970146 1.230182 1.250703 1.346278479 1.180497 1.248452 1.279710732 1.234643 1.233206 1.359003846 1.177607 1.207667 1.285088932

RI PT

h_exp-0.2l 1090.419 1816.499 2179.715 2677.686 2950.823 3474.048 3867.521 4636.501 4979.387

SC

Re^0.8 Pr^0.4 Pe 12902.1264 72085.25 20590.1435 129029.1 28553.2441 188025.5 33282.4345 231137 37719.4422 267611.9 41666.9541 307506 49399.4289 374652.4 54765.8073 435952.8 62745.437 511129.2

M AN U

13.241 13.352 15.18486 14.30861 14.8869 14.04574 14.93123 13.63922 14.24912

TE D

Pr

EP

Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561

AC C

RE 5444.095 9663.65 12382.43 16153.7 17976.33 21893.18 25091.86 31963.17 35870.93

0.2% 50nm0.2% 50nm0.2% 50nm 1.176226 1.153275 1.301406 1.193207 1.176698 1.318999 1.072299 1.143413 1.156355 1.109216 1.140394 1.209465 1.072065 1.129403 1.160439 1.117188 1.135824 1.222621 1.099887 1.163201 1.192325 1.151444 1.150105 1.267425 1.096179 1.12416 1.196228

ACCEPTED MANUSCRIPT

Nu_exp-0.3sNu_DB 67.6355 64.03218 102.797 88.42092 126.7817 114.3404 156.1554 137.6449 174.9715 159.5505 222.3501 196.6073 248.0932 223.3202 286.7741 251.8322 314.4038 271.8178

Nu_Gen 51.22818 77.12423 104.0727 130.0495 153.8867 195.9333 226.02 259.8369 282.7461

(Hnf/Hpf)V 1.185641083 1.329027593 1.195267188 1.252527278 1.180590009 1.229592283 1.185193237 1.248724405 1.252069608

M AN U TE D

(Hnf/Hpf)Re 1.254279776 1.374293179 1.332620188 1.353085775 1.31848137 1.355397074 1.340037919 1.359803446 1.388479936

RI PT

h_exp-0.3s K 1130.946 0.128753 1738.584 0.130228 2071.507 0.125812 2585.771 0.127504 2856.874 0.125723 3650.063 0.126402 4031.153 0.125114 4730.886 0.127026 5148.601 0.126093

SC

Pr Re^0.8 Pr^0.4 Pe 14.21163 13685.3757 76235.97 13.65727 18452.0874 111870.6 15.51732 25760.9561 164436.5 14.7233 30049.3645 201972.8 15.55859 36004.1494 249717 15.22936 43800.6874 320760.4 15.87839 51013.3747 384063.8 14.90663 55387.4257 432433.3 15.38466 60926.0106 483316.3

EP

Vel 0.749289 1.112027 1.580575 1.966943 2.398989 3.09715 3.671456 4.201294 4.654405

AC C

RE 5364.338 8191.285 10596.97 13717.9 16050.11 21061.97 24187.83 29009.45 31415.48

(Hnf/Hpf)Pe 1.337506581 1.51288134 1.324554106 1.402612492 1.307718957 1.367532613 1.307640674 1.395690271 1.389587622

0.3% 13nm 0.3% 13nm 0.3% 13nm 1.048587 1.109291 1.182897 1.16447 1.204131 1.32556 1.050256 1.170945 1.163857 1.086559 1.173792 1.216757 1.031577 1.152064 1.14266 1.079922 1.190414 1.201072 1.029352 1.163836 1.135699 1.089969 1.186926 1.218251 1.123628 1.246045 1.247039

ACCEPTED MANUSCRIPT

K 0.102582 0.126427 0.123222 0.124255 0.124042 0.124885 0.124227 0.126915 0.125735

Nu_exp-0.3lNu_DB 85.99118 67.21606 120.1099 102.416 150.6336 132.1555 188.1594 158.9348 188.3668 170.0043 239.7737 202.3768 255.5954 220.067 284.4845 248.5357 312.3335 275.2068

Nu_Gen 54.71687 92.06135 123.5585 153.6267 165.9727 203.0339 223.0541 257.2314 287.9402

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.178051 1.195691 1.306495845 1.32676 1.351873 1.474992721 1.224673 1.340405 1.334858122 1.294313 1.382152 1.420067544 1.207024 1.295278 1.322774477 1.308613 1.377506 1.441560308 1.269144 1.356096 1.392390322 1.304148 1.315634 1.454974513 1.270445 1.312958 1.406691714

RI PT

h_exp-0.3l 1145.606 1972.101 2410.568 3036.336 3034.471 3888.86 4123.626 4689.025 5100.145

M AN U

SC

Re^0.8 Pr^0.4 Pe 14105.5796 79778.58 21516.0126 135176.6 29731.7483 196826.1 34929.1963 243096.3 37532.066 265444.5 43867.2776 325060.5 48387.8929 365279.5 51687.2146 405986.3 58611.4662 470388.7

TE D

Pr 13.78509 13.8103 15.48003 14.88776 15.0009 14.54944 14.89987 13.57908 14.12815

EP

Vel 0.767586 1.304545 1.853157 2.307685 2.51621 3.101358 3.467357 3.935347 4.516705

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

0.3% 50nm0.3% 50nm0.3% 50nm 1.07283 1.088895 1.189802 1.197519 1.220186 1.331312 1.092166 1.195376 1.190429 1.155977 1.234428 1.268291 1.071911 1.150286 1.174704 1.167418 1.228876 1.28602 1.112423 1.188638 1.22045 1.157526 1.167722 1.291397 1.108565 1.145661 1.227452

ACCEPTED MANUSCRIPT

Nu_Gen 52.01392 109.5255 126.9408 149.2917 161.4681 182.3632 209.2581 236.2014 272.1572

(Hnf/Hpf)V 1.370130052 1.296301535 1.283756653 1.324405837 1.289846457 1.346430765 1.318479734 1.353072011 1.340044821

(Hnf/Hpf)Re 1.537441677 1.513339277 1.592212691 1.582594713 1.55742004 1.551848589 1.543975997 1.500626002 1.532098163

(Hnf/Hpf)Pe0.5% 13nm 1.599731 1.489318 1.447077 1.5095 1.465359 1.554578 1.51327 1.589468 1.552256

RI PT

Nu_exp-0.5sNu_DB 79.47883 64.97121 142.8185 119.4484 168.6683 136.156 193.8406 155.8581 203.7651 166.9166 227.138 184.7466 254.3888 208.6477 276.3672 231.0418 319.2169 262.5832

SC

h_exp-0.5s K 1389.448 0.134611 2445.348 0.13184 2818.264 0.128659 3284.955 0.130489 3438.53 0.129937 3912.965 0.13265 4349.012 0.131639 4865.766 0.135567 5521.925 0.133197

M AN U

Re^0.8 Pr^0.4 Pe 14144.63 78838.83 27114.33 174758.2 32807.68 216325.8 36219.19 248522.8 39187.97 273075.1 41381.97 298100.7 47507.67 351834.9 49632.14 380732.8 58319.86 459362

TE D

Pr 14.65539 15.71246 17.3558 16.33912 16.62016 15.36753 15.79295 14.33289 15.15173

EP

Vel 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418

AC C

RE 5379.509 11122.27 12464.18 15210.3 16430.35 19398.08 22277.97 26563.57 30317.47

1.058302489 1.099738065 1.108348345 1.135471921 1.101384653 1.176735755 1.143075549 1.138414644 1.156510411

0.5% 13nm0.5% 13nm 1.187536 1.235649 1.283865 1.263487 1.374658 1.249353 1.356829 1.294162 1.329863 1.251252 1.356264 1.358649 1.338573 1.311951 1.26256 1.337308 1.32226 1.339657

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

RE Vel Pr Re^0.8 Pr^0.4 Pe h_exp-0.5l K Nu_exp-0.5lNu_DB Nu_Gen (Hnf/Hpf)V (Hnf/Hpf)Re (Hnf/Hpf)Pe0.5% 50nm 4922.87805 0.699653673 14.59087644 13117.66821 71829.10536 1284.608568 0.128112 77.2099 60.41373 47.33686322 1.422590845 1.525969862 1.593409 9750.402834 1.369898174 14.33141543 22259.076 139737.0737 2046.873625 0.128373 122.7747 103.6243 93.08967541 1.324207643 1.407418926 1.490866 13180.32319 2.081466016 16.62645037 32865.51092 219141.9895 2971.416699 0.124479 183.8058 139.955 131.5091157 1.375573466 1.605362507 1.51001 18148.94292 2.845290758 16.48304217 42084.13815 299149.7916 3849.468936 0.124687 237.7217 180.1457 176.4150658 1.387762624 1.610164159 1.525059 20828.32383 3.363085294 17.08011992 48687.1522 355750.2688 4210.704877 0.123891 261.7002 204.0082 203.0491413 1.327945304 1.577544977 1.45223 24946.99404 3.911925305 16.48847461 54299.40348 411337.8779 5065.259953 0.124683 312.8139 232.3885 235.9882169 1.415484068 1.64262173 1.555391 29650.52862 4.804751989 17.15686942 64873.00241 508710.2476 5982.985833 0.123804 372.1111 271.0997 280.3462331 1.418393995 1.689827704 1.550024

0.5% 50nm 1.120787317 1.123796049 1.18396894 1.210760282 1.123654624 1.237425533 1.230750039

1.202234411 1.194413758 1.381750515 1.404795588 1.334855963 1.43599078 1.466274899

0.5% 50nm 1.255366 1.265231 1.29968 1.330545 1.228819 1.359733 1.344966

ACCEPTED MANUSCRIPT

8000

RI PT

7000

SC

5000 4000

M AN U

Pressure drop (Pa)

6000

3000

Mcadams Correlation

TE D

2000

Pure kerosene

1000

EP

0

AC C

0

2000

4000

Blasius

6000

8000

Re

10000

12000

14000

ACCEPTED MANUSCRIPT

VISCOSITY Pa.s 0.00135 0.00135 0.00135 0.00135 0.00135 0.00135 0.00135

REYNOLDS NUMBER (Re) 11820.39583 8939.795162 7675.581705 6230.766325 4876.251906 3431.436527 2131.102685

FRICTION FACTOR (f) Blasius 0.030306032 0.032497892 0.03376053 0.035567367 0.037815126 0.041287453 0.046508891

FRICTION FACTOR (f) McAdams 0.028202747 0.029823067 0.030746491 0.032056015 0.033666704 0.036117911 0.039728022

FRICTION FACTOR (f) Hadland 0.074960098 0.077804707 0.079460405 0.081852376 0.084867583 0.089620017 0.097014415

PRESSURE DROP Mcadams 7071.797831 5175.677334 3933.488723 2702.416018 1738.331543 923.4945079 391.8009173

RI PT

VELOCTY m/sec 2.555498496 2.12600295 1.825356069 1.481759632 1.159637973 0.816041537 0.506804744

M AN U

SC

Area m^2 4.65663E-05 4.65663E-05 4.65663E-05 4.65663E-05 4.65663E-05 4.65663E-05 4.65663E-05

TE D

kg/m^3 810.96 810.96 810.96 810.96 810.96 810.96 810.96

MASS FLOW RATE kg/sec 0.09650424 0.08028504 0.0689316 0.05595624 0.04379184 0.03081648 0.019138656

EP

DENSITY

AC C

rpm 1440 1200 1000 850 625 400 250

VOLUME FLOW RATE m^3/s 0.000119 0.000099 0.000085 0.000069 0.000054 0.000038 0.0000236

PRESSURE DROP Blasius 7608.199811 5646.567046 4324.202451 3001.987002 1954.843427 1056.925054 459.2180011

PRESSURE DROP Hadland 188.1841233 135.1870739 101.7765059 69.08573506 43.8720838 22.94199212 9.578978193

measured 185 139 107 74 47 21 11

7400 5600 4400 3200 2100 1000 500

ACCEPTED MANUSCRIPT

0.045

0.05% 13nm

RI PT

0.04

0.035

+12%

M AN U

0.03

SC

0.2% 13nm

0.025

0.2% 50nm 0.3% 13nm 0.3% 50nm

-12%

0.015

0.5% 13nm

10000 20000 30000 40000 50000 60000 70000

EP

0

TE D

0.02

AC C

Friction factor

0.05% 50nm

Re

ACCEPTED MANUSCRIPT

0.80 1.29 1.80 2.23 2.66 3.07 3.42 3.97 4.58 Vel 0.70 1.26 1.56 2.31 2.75 3.18 3.28 4.03 4.73

H 329.594 679.478 1183.04 1636.336 2059.792 2462.359 2849.026 3222.952 3586.306 3940.664 4287.216 4626.894 4960.442 5288.47 5611.485 5929.914 6244.122 888.0548 1536.526 1841.624 2463.771 2424.544 2806.421 3320.008 3641.717 4097.511 #VALUE! 888.0548 1447.366 1894.37 2244.16 2586.982 2904.682 3165.46 3561.468 3994.658 #VALUE! 891.291 1425.054 1690.124 2312.586 2655.211 2981.576 3059.105 3605.963 4104.4

RI PT

Nu 24.17023 50.30751 87.59046 121.1518 152.5038 182.3093 210.9375 238.6224 265.5246 291.7607 317.4189 342.5681 367.2635 391.5502 415.4657 439.0417 462.3052 65.75021 113.762 136.351 182.4138 179.5095 207.7831 245.8083 269.6272 303.3734 #VALUE! 65.75021 107.1607 140.2562 166.1542 191.5361 215.0582 234.3658 263.6856 295.7584 #VALUE! 65.98982 105.5088 125.1342 171.2203 196.5877 220.7513 226.4915 266.9799 303.8835

SC

Pe 23304.19 58260.47 116520.9 174781.4 233041.9 291302.3 349562.8 407823.3 466083.8 524344.2 582604.7 640865.2 699125.6 757386.1 815646.6 873907 932167.5 81415 161558.4 202607.8 291511.2 285721 343040.8 423232.1 475102.7 550560.2 #VALUE! 81415 149926.2 209887.1 259401.3 309846.4 358119.5 398750 462052.1 533340.2 #VALUE! 81786.03 147042.8 181992.3 269325.2 320094.7 370008.8 382074.3 469279.1 551717.6

M AN U

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

TE D

Vel

Re Pr 1536.202 3840.506 7681.011 11521.52 15362.02 19202.53 23043.03 26883.54 30724.04 34564.55 38405.06 42245.56 46086.07 49926.57 53767.08 57607.58 61448.09 5366.843 10649.86 13355.82 19216.29 18834.61 22613.1 27899.28 31318.57 36292.7 #VALUE! 5366.843 9883.071 13835.67 17099.62 20424.94 23607.08 26285.43 30458.28 35157.56 #VALUE! 5391.301 9692.999 11996.86 17753.8 21100.51 24390.82 25186.17 30934.68 36368.99

EP

0.20 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 0.70 1.39 1.74 2.50 2.45 2.94 3.63 4.08 4.72

AC C

V

#VALUE! 948.068 1494.933 1849.591 2302.415 2485.954 2743.895 2933.17 3570.648 3966.328 #VALUE! 808.6815 1441.913 1677.676 2131.788 2409.405 2731.215 3182.288 3675.899 4093.567 #VALUE! 880.739 1401.932 1848.404 2204.555 2460.67 2780.331 3225.505 3697.252 4162.99 939.1149 1287.928 1706.285 2032.511 2382.44 2922.599 3348.653 3729.974 4048.468 957.4169 1463.412 1937.89 2309.62 2475.124 2925.775 3198.882 3539.858

SC

#VALUE! 70.1935 110.6826 136.9409 170.4673 184.0562 203.1538 217.1674 264.3653 293.6608 #VALUE! 59.87353 106.7571 124.2126 157.8343 178.3886 202.215 235.6117 272.1579 303.0814 #VALUE! 65.20856 103.7969 136.853 163.2219 182.1842 205.8514 238.8114 273.7388 308.2214 69.53063 95.35623 126.3307 150.484 176.3922 216.3847 247.9291 276.1615 299.7424 70.88568 108.3488 143.4784 171.0007 183.2544 216.6199 236.8403 262.0856

M AN U

#VALUE! 88349.5 156110.4 203703.9 267845.4 294795.7 333514.1 362515.3 463541.5 528616.3 #VALUE! 72423.01 149220.6 180318.3 243267.8 283492.8 331588.7 401401.6 480683.5 549897.9 #VALUE! 80577.5 144066.6 203540.6 253691.5 291052.6 339059 408227.1 484176.3 561579.8 87307.82 129574.4 184170.1 229190.1 279532.4 360882.9 427801.6 489538.7 542335.7 89439.86 152006.8 215931.6 268893.6 293191.2 361373.2 404019.7 458550.3

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

#VALUE! 5823.962 10290.73 13428.08 17656.26 19432.81 21985.11 23896.86 30556.46 34846.16 #VALUE! 4774.094 9836.557 11886.51 16036.11 18687.72 21858.18 26460.23 31686.46 36249.04 #VALUE! 5311.635 9496.808 13417.31 16723.24 19186.06 22350.63 26910.16 31916.7 37019.1 5755.295 8541.493 12140.41 15108.11 18426.66 23789.25 28200.5 32270.18 35750.54 5895.838 10020.23 14234.12 17725.35 19327.04 23821.57 26632.81 30227.45

AC C

Vel 0.758229 1.339763 1.748217 2.298689 2.52998 2.862267 3.11116 3.978182 4.536663 Vel 0.62 1.28 1.55 2.09 2.43 2.85 3.44 4.13 4.72 Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561 0.75 1.11 1.58 1.97 2.40 3.10 3.67 4.20 4.65 0.77 1.30 1.85 2.31 2.52 3.10 3.47 3.94

RI PT

ACCEPTED MANUSCRIPT

3952.363 998.3795 1857.162 2161.295 2441.875 2624.52 2861.127 3247.374 3540.343 4056.825 889.0085 1521.774 2126.644 2730.868 3121.689 3522.993 4152.754 922.0801 1565.064 1679.369 2249.668 2227.969 2716.355 3066.233 3597.444 4107.391 1048.957 1534.846 1779.974 2223.705 2342.924 2874.383 3095.506 3686.68 3988.522 914.2035 1454.451 1555.335 2199.68 2436.893 2900.474 2917.17 3607.21 3976.339 1004.491 1568.337 1752.876

SC

292.6269 73.91849 137.5014 160.0189 180.7927 194.3154 211.8334 240.4306 262.1216 300.3611 65.82082 112.6698 157.4535 202.1893 231.1251 260.837 307.4635 68.26939 115.875 124.3379 166.562 164.9554 201.1147 227.0192 266.3492 304.1049 77.66317 113.6377 131.7865 164.6397 173.4665 212.8149 229.1865 272.9561 295.304 67.68622 107.6853 115.1546 162.8609 180.4238 214.7467 215.9827 267.0723 294.402 74.371 116.1173 129.7803

M AN U

526290.7 94248.47 204746.7 247484.1 288276.4 315476.6 351419.7 411689.8 458628.9 543735.4 81524.3 159621.8 242534.4 331535.9 391869.9 455821.2 559854.2 85332.71 165317.9 180545.8 260197.3 257064 329335 383187.4 467893.8 552220.2 100254 161337.7 194165.4 256449.1 273749 353456.2 387765.5 482446.4 532316.2 84422.53 150844.2 164034.4 252990.5 287541.3 357471.2 360045 469482.1 530284.5 94970.23 165750.2 190477.5

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

34692.86 6212.82 13496.81 16314.04 19003.06 20796.08 23165.44 27138.42 30232.63 35842.8 5374.048 10522.2 15987.76 21854.71 25831.9 30047.54 36905.35 5625.096 10897.69 11901.5 17152.1 16945.55 21709.62 25259.55 30843.37 36402.12 6608.704 10635.31 12799.3 16905.02 18045.42 23299.68 25561.34 31802.66 35090.06 5565.097 9943.588 10813.08 16677.03 18954.6 23564.35 23734.02 30948.06 34956.13 6260.398 10926.18 12556.2

AC C

4.52 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418 0.70 1.37 2.08 2.85 3.36 3.91 4.80

RI PT

ACCEPTED MANUSCRIPT

SC

2257.352 2365.024 2768.268 2927.392 3553.058 3961.52 803.2339 1420.566 1499.242 1965.644 2151.631 2579.476 2883.869 3438.884 3743.633 902.7711 1428.844 1703.752 2108.964 2296.182 2705.142 3015.379 3662.634 3992.714 885.5582 1219.384 1485.108 1828.159 2069.969 2588.067 2903.419 3362.635 3600.096 937.577 1421.87 1731.072 2127.646 2306.481 2735.096 2961.279 3457.199 3769.163 898.955 1552.341 1696.466 2012.643 2106.711

M AN U

167.1308 175.1027 204.9583 216.7396 263.0629 293.3049 59.4702 105.1765 111.0015 145.5332 159.3034 190.9804 213.5173 254.6097 277.1729 66.83978 105.7894 126.1432 156.1444 170.0058 200.2846 223.254 271.1758 295.6144 65.56537 90.28131 109.9551 135.3541 153.2573 191.6165 214.9647 248.9643 266.5456 69.41676 105.2731 128.1659 157.5277 170.7683 202.5023 219.2485 255.9657 279.063 66.55724 114.9329 125.6037 149.013 155.9776

TE D

261308.6 276980.4 337221.2 361622.8 460688.7 527815.4 71813.69 146464.2 156673 219804.1 246101.6 308723.1 354914.9 442259 491780.6 83104.93 147531.8 183828.5 240016.5 266939.4 327636.5 375259.8 478516.1 533015.7 81129 121012.5 154829 200757.6 234482 310008.9 357924.9 430035.5 468325 87129.13 146632.3 187520.5 242677.2 268436.8 332177.6 366862.9 445205.2 495976.2 82666.04 163639.6 182846.3 226393.1 239696.1

EP

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

AC C

17225.35 18258.43 22229.48 23838.02 30368.41 34793.37 4733.928 9654.858 10327.82 14489.39 16222.91 20350.89 23395.84 29153.53 32417.97 5478.242 9725.234 12117.9 15821.79 17596.53 21597.66 24736.97 31543.58 35136.17 5347.989 7977.094 10206.26 13233.86 15456.95 20435.66 23594.26 28347.76 30871.78 5743.516 9665.941 12361.27 15997.18 17695.24 21897.01 24183.45 29347.74 32694.54 5449.311 10787.06 12053.15 14923.74 15800.66

RI PT

ACCEPTED MANUSCRIPT

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

286166.1 327696.2 388219.8 452039.2 74314.91 142951.1 197652.6 268687.9 310975.8 374645.1 448248.3

179.7332 200.3137 229.4012 259.1042 61.12155 103.1534 133.6767 170.8961 192.0945 222.9614 257.3645

2427.565 2705.536 3098.406 3499.589 825.5378 1393.241 1805.503 2308.206 2594.523 3011.427 3476.091

AC C

EP

TE D

M AN U

SC

18863.95 21601.59 25591.28 29798.23 4898.807 9423.274 13029.18 17711.79 20499.4 24696.45 29548.34

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

prdrop_hadla nd

Re

0.017416495 0.050248043 0.101711693 0.17092171 0.262813962 0.313521108 0.341532226 0.406619735 0.488341043

Pr 5000 10000 15000 20000 25000 30000 35000

15.9 15.9 15.9 15.9 15.9 15.9 15.9

Nu_Dittus Boelter RePR Nu_Sonawane 14473.49 63.3086 67.60822657 25199.8 110.2267 117.7127594 34855.4 152.4613 162.8158001 43875.4 191.9158 204.9498181 52450.44 229.4239 245.0053386 60686.78 265.4506 283.4787731 68651.74 300.2902 320.6845051

Blasius Sonawane Present correlation 0.037579 0.037864224 0.039153156 0.0316 0.033191996 0.033615547 0.028554 0.030730953 0.030746813 0.026572 0.029096293 0.028861147 0.025131 0.027888475 0.027478523 0.024011 0.026938929 0.026398151 0.023103 0.026161367 0.025517916

12% 0.043851535 0.037649412 0.03443643 0.032324484 0.030775945 0.029565929 0.028580066

-12% Present Correlation 0.034454778 72.36742707 0.029581681 125.9990088 0.027057195 174.2770243 0.025397809 219.3770162 0.0241811 262.2521973 0.023230373 303.4339233 0.022455766 343.2587085

AC C

EP

TE D

M AN U

SC

RI PT

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04601731 73.228819 60.5341941 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8333743 114.02112 103.854921 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6091968 145.27525 136.771494 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5438912 184.39553 180.878658 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9080838 216.74782 216.986307 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1383667 241.10514 246.006532 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2960579 247.95851 253.655111 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575419 277.97486 290.119402 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7894632 294.97439 309.411637 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718015 4523.427 42245.56 5.5 15.9 671704.4 0.105

20% 86.84091248 151.1988106 209.1324291 263.2524194 314.7026367 364.120708 411.9104502

-20% 57.89394166 100.799207 139.4216194 175.5016129 209.8017578 242.7471387 274.6069668

0 550000 550000 550000 550000 550000 550000 550000

0 40000 40000 40000 40000 40000 40000 40000

0 5 5 5 5 5 5 5

1 1 1 1 1 1 1 1

ACCEPTED MANUSCRIPT

RI PT

0.0373168 0.0338451 0.0318496 0.0282757 0.0290005 0.0276256 0.0266313 0.0242645 0.0236647

AC C

EP

TE D

M AN U

SC

RE Nu_exp-0.05s 5547.646 65.07888109 10667.36 110.7126768 12270.8 126.870515 17818.39 167.9756577 17469.05 167.5351509 21709.62 199.861825 25259.55 236.2631742 31067.9 257.8731867 36140.99 286.6818333

f_measur ed

ACCEPTED MANUSCRIPT

RI PT

0.036741 0.034585 0.030481 0.029408 0.027605 0.02645 0.026002 0.025158 0.0241

EP

TE D

M AN U

SC

75.93648 112.1558 140.3751 168.7731 185.5256 224.8539 246.1604 276.9776 316.0861

AC C

RE 6340.269 10563.44 13191.82 17152.91 18753.23 23641.72 25750.78 32135.73 35090.06

f_measu Nu_exp-0.5l red

ACCEPTED MANUSCRIPT

RI PT

0.04218 0.034254 0.031944 0.028686 0.028225 0.02576 0.026575 0.024662 0.023752

EP

TE D

M AN U

SC

63.78673 101.5692 119.4241 168.9436 187.4891 219.6312 223.0068 268.9232 304.0191

AC C

RE 5528.036 10010.13 10975.09 16677.03 19239.19 23732.43 24252.75 31054.79 34706.18

f_measu Nu_exp-0.1s red

ACCEPTED MANUSCRIPT

RI PT

0.036146 0.033284 0.030597 0.028512 0.028001 0.027585 0.026836 0.025112 0.024737

EP

TE D

M AN U

SC

76.10325 116.2627 136.5566 171.6956 187.2706 217.0887 229.5167 284.2824 312.0883

AC C

RE 5970.25 10637.36 12836.75 17473.84 18665.19 22229.48 23838.02 30584 34793.37

f_measu Nu_exp-0.1l red

ACCEPTED MANUSCRIPT

RI PT

0.040188 0.036288 0.035656 0.032057 0.030599 0.029396 0.028127 0.026912 0.026489

EP

TE D

M AN U

SC

61.4864 101.3997 117.0625 144.1866 165.7678 190.284 221.3851 263.1293 285.8465

AC C

RE 4733.928 9593.626 10626.95 14996.81 16811.26 20627.44 24148.21 29555.64 33106.89

f_measu Nu_exp-0.2s red

ACCEPTED MANUSCRIPT

RI PT

0.043287 0.035546 0.03392 0.03166 0.031104 0.029337 0.027827 0.026376 0.025733

EP

TE D

M AN U

SC

66.72749 111.4692 138.1021 167.2666 186.1079 216.0257 243.429 292.318 316.9715

AC C

RE 5444.095 9663.65 12382.43 16153.7 17976.33 21893.18 25091.86 31963.17 35870.93

f_measu Nu_exp-0.2l red

ACCEPTED MANUSCRIPT

RI PT

0.04132 0.039604 0.036113 0.034645 0.032695 0.030365 0.029257 0.027892 0.027248

EP

TE D

M AN U

SC

67.6355 102.797 126.7817 156.1554 174.9715 222.3501 248.0932 286.7741 311.3505

AC C

RE 5364.338 8191.285 10596.97 13717.9 16050.11 21061.97 24187.83 29009.45 31415.48

f_measu Nu_exp-0.3s red

ACCEPTED MANUSCRIPT

RI PT

0.043749 0.037865 0.035277 0.032914 0.032163 0.029747 0.028515 0.027795 0.027292

EP

TE D

M AN U

SC

75.6161 126.2003 156.8825 188.1594 188.3668 239.7737 255.5954 300.8655 330.7055

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

f_measu Nu_exp-0.3l red

ACCEPTED MANUSCRIPT

EP

TE D

M AN U

SC

RI PT

Nu_exp-0.5sf_measured 79.47883 0.046918031 142.8185 0.037280862 168.6683 0.036857518 193.8406 0.033851207 203.7651 0.034197865 227.138 0.031778508 254.3888 0.030736776 276.3672 0.029885658 319.2169 0.028428072

AC C

RE 5379.509 11122.27 12464.18 15210.3 16430.35 19398.08 22277.97 26563.57 30317.47

ACCEPTED MANUSCRIPT

RI PT

0.04703 0.038166 0.035425 0.031597 0.031437 0.029085 0.028366

AC C

EP

TE D

M AN U

SC

RE Nu_exp-0.5l 4922.878 77.20989627 9750.403 122.7747195 13180.32 183.8057726 18148.94 237.7216507 20828.32 261.7002016 24946.99 312.8139128 29650.53 372.1110812

f_measu red

ACCEPTED MANUSCRIPT

1.8

0.5% 50nm 1.7

RI PT

0.5% 13nm 1.6

0.3% 13nm

SC

1.4 1.3

M AN U

Merit Number

0.3% 50nm

1.5

1.2 1.1

0.9

10000

AC C

EP

0

TE D

1

20000

30000

Re

0.2% 50nm 0.2% 13nm 0.05% 50nm 0.05% 13nm

40000

50000

60000

ACCEPTED MANUSCRIPT

0.80 1.29 1.80 2.23 2.66 3.07 3.42 3.97 4.58 Vel 0.70 1.26 1.56 2.31 2.75 3.18 3.28 4.03 4.73

H 329.594 679.478 1183.04 1636.336 2059.792 2462.359 2849.026 3222.952 3586.306 3940.664 4287.216 4626.894 4960.442 5288.47 5611.485 5929.914 6244.122 888.0548 1536.526 1841.624 2463.771 2424.544 2806.421 3320.008 3641.717 4097.511 #VALUE! 888.0548 1447.366 1894.37 2244.16 2586.982 2904.682 3165.46 3561.468 3994.658 #VALUE! 891.291 1425.054 1690.124 2312.586 2655.211 2981.576 3059.105 3605.963 4104.4

RI PT

Nu 24.17023 50.30751 87.59046 121.1518 152.5038 182.3093 210.9375 238.6224 265.5246 291.7607 317.4189 342.5681 367.2635 391.5502 415.4657 439.0417 462.3052 65.75021 113.762 136.351 182.4138 179.5095 207.7831 245.8083 269.6272 303.3734 #VALUE! 65.75021 107.1607 140.2562 166.1542 191.5361 215.0582 234.3658 263.6856 295.7584 #VALUE! 65.98982 105.5088 125.1342 171.2203 196.5877 220.7513 226.4915 266.9799 303.8835

SC

Pe 23304.19 58260.47 116520.9 174781.4 233041.9 291302.3 349562.8 407823.3 466083.8 524344.2 582604.7 640865.2 699125.6 757386.1 815646.6 873907 932167.5 81415 161558.4 202607.8 291511.2 285721 343040.8 423232.1 475102.7 550560.2 #VALUE! 81415 149926.2 209887.1 259401.3 309846.4 358119.5 398750 462052.1 533340.2 #VALUE! 81786.03 147042.8 181992.3 269325.2 320094.7 370008.8 382074.3 469279.1 551717.6

M AN U

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

TE D

Vel

Re Pr 1536.202 3840.506 7681.011 11521.52 15362.02 19202.53 23043.03 26883.54 30724.04 34564.55 38405.06 42245.56 46086.07 49926.57 53767.08 57607.58 61448.09 5366.843 10649.86 13355.82 19216.29 18834.61 22613.1 27899.28 31318.57 36292.7 #VALUE! 5366.843 9883.071 13835.67 17099.62 20424.94 23607.08 26285.43 30458.28 35157.56 #VALUE! 5391.301 9692.999 11996.86 17753.8 21100.51 24390.82 25186.17 30934.68 36368.99

EP

0.20 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 0.70 1.39 1.74 2.50 2.45 2.94 3.63 4.08 4.72

AC C

V

#VALUE! 948.068 1494.933 1849.591 2302.415 2485.954 2743.895 2933.17 3570.648 3966.328 #VALUE! 808.6815 1441.913 1677.676 2131.788 2409.405 2731.215 3182.288 3675.899 4093.567 #VALUE! 880.739 1401.932 1848.404 2204.555 2460.67 2780.331 3225.505 3697.252 4162.99 939.1149 1287.928 1706.285 2032.511 2382.44 2922.599 3348.653 3729.974 4048.468 957.4169 1463.412 1937.89 2309.62 2475.124 2925.775 3198.882 3539.858

SC

#VALUE! 70.1935 110.6826 136.9409 170.4673 184.0562 203.1538 217.1674 264.3653 293.6608 #VALUE! 59.87353 106.7571 124.2126 157.8343 178.3886 202.215 235.6117 272.1579 303.0814 #VALUE! 65.20856 103.7969 136.853 163.2219 182.1842 205.8514 238.8114 273.7388 308.2214 69.53063 95.35623 126.3307 150.484 176.3922 216.3847 247.9291 276.1615 299.7424 70.88568 108.3488 143.4784 171.0007 183.2544 216.6199 236.8403 262.0856

M AN U

#VALUE! 88349.5 156110.4 203703.9 267845.4 294795.7 333514.1 362515.3 463541.5 528616.3 #VALUE! 72423.01 149220.6 180318.3 243267.8 283492.8 331588.7 401401.6 480683.5 549897.9 #VALUE! 80577.5 144066.6 203540.6 253691.5 291052.6 339059 408227.1 484176.3 561579.8 87307.82 129574.4 184170.1 229190.1 279532.4 360882.9 427801.6 489538.7 542335.7 89439.86 152006.8 215931.6 268893.6 293191.2 361373.2 404019.7 458550.3

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

#VALUE! 5823.962 10290.73 13428.08 17656.26 19432.81 21985.11 23896.86 30556.46 34846.16 #VALUE! 4774.094 9836.557 11886.51 16036.11 18687.72 21858.18 26460.23 31686.46 36249.04 #VALUE! 5311.635 9496.808 13417.31 16723.24 19186.06 22350.63 26910.16 31916.7 37019.1 5755.295 8541.493 12140.41 15108.11 18426.66 23789.25 28200.5 32270.18 35750.54 5895.838 10020.23 14234.12 17725.35 19327.04 23821.57 26632.81 30227.45

AC C

Vel 0.758229 1.339763 1.748217 2.298689 2.52998 2.862267 3.11116 3.978182 4.536663 Vel 0.62 1.28 1.55 2.09 2.43 2.85 3.44 4.13 4.72 Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561 0.75 1.11 1.58 1.97 2.40 3.10 3.67 4.20 4.65 0.77 1.30 1.85 2.31 2.52 3.10 3.47 3.94

RI PT

ACCEPTED MANUSCRIPT

3952.363 998.3795 1857.162 2161.295 2441.875 2624.52 2861.127 3247.374 3540.343 4056.825 889.0085 1521.774 2126.644 2730.868 3121.689 3522.993 4152.754 922.0801 1565.064 1679.369 2249.668 2227.969 2716.355 3066.233 3597.444 4107.391 1048.957 1534.846 1779.974 2223.705 2342.924 2874.383 3095.506 3686.68 3988.522 914.2035 1454.451 1555.335 2199.68 2436.893 2900.474 2917.17 3607.21 3976.339 1004.491 1568.337 1752.876

SC

292.6269 73.91849 137.5014 160.0189 180.7927 194.3154 211.8334 240.4306 262.1216 300.3611 65.82082 112.6698 157.4535 202.1893 231.1251 260.837 307.4635 68.26939 115.875 124.3379 166.562 164.9554 201.1147 227.0192 266.3492 304.1049 77.66317 113.6377 131.7865 164.6397 173.4665 212.8149 229.1865 272.9561 295.304 67.68622 107.6853 115.1546 162.8609 180.4238 214.7467 215.9827 267.0723 294.402 74.371 116.1173 129.7803

M AN U

526290.7 94248.47 204746.7 247484.1 288276.4 315476.6 351419.7 411689.8 458628.9 543735.4 81524.3 159621.8 242534.4 331535.9 391869.9 455821.2 559854.2 85332.71 165317.9 180545.8 260197.3 257064 329335 383187.4 467893.8 552220.2 100254 161337.7 194165.4 256449.1 273749 353456.2 387765.5 482446.4 532316.2 84422.53 150844.2 164034.4 252990.5 287541.3 357471.2 360045 469482.1 530284.5 94970.23 165750.2 190477.5

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

34692.86 6212.82 13496.81 16314.04 19003.06 20796.08 23165.44 27138.42 30232.63 35842.8 5374.048 10522.2 15987.76 21854.71 25831.9 30047.54 36905.35 5625.096 10897.69 11901.5 17152.1 16945.55 21709.62 25259.55 30843.37 36402.12 6608.704 10635.31 12799.3 16905.02 18045.42 23299.68 25561.34 31802.66 35090.06 5565.097 9943.588 10813.08 16677.03 18954.6 23564.35 23734.02 30948.06 34956.13 6260.398 10926.18 12556.2

AC C

4.52 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418 0.70 1.37 2.08 2.85 3.36 3.91 4.80

RI PT

ACCEPTED MANUSCRIPT

SC

2257.352 2365.024 2768.268 2927.392 3553.058 3961.52 803.2339 1420.566 1499.242 1965.644 2151.631 2579.476 2883.869 3438.884 3743.633 902.7711 1428.844 1703.752 2108.964 2296.182 2705.142 3015.379 3662.634 3992.714 885.5582 1219.384 1485.108 1828.159 2069.969 2588.067 2903.419 3362.635 3600.096 937.577 1421.87 1731.072 2127.646 2306.481 2735.096 2961.279 3457.199 3769.163 898.955 1552.341 1696.466 2012.643 2106.711

M AN U

167.1308 175.1027 204.9583 216.7396 263.0629 293.3049 59.4702 105.1765 111.0015 145.5332 159.3034 190.9804 213.5173 254.6097 277.1729 66.83978 105.7894 126.1432 156.1444 170.0058 200.2846 223.254 271.1758 295.6144 65.56537 90.28131 109.9551 135.3541 153.2573 191.6165 214.9647 248.9643 266.5456 69.41676 105.2731 128.1659 157.5277 170.7683 202.5023 219.2485 255.9657 279.063 66.55724 114.9329 125.6037 149.013 155.9776

TE D

261308.6 276980.4 337221.2 361622.8 460688.7 527815.4 71813.69 146464.2 156673 219804.1 246101.6 308723.1 354914.9 442259 491780.6 83104.93 147531.8 183828.5 240016.5 266939.4 327636.5 375259.8 478516.1 533015.7 81129 121012.5 154829 200757.6 234482 310008.9 357924.9 430035.5 468325 87129.13 146632.3 187520.5 242677.2 268436.8 332177.6 366862.9 445205.2 495976.2 82666.04 163639.6 182846.3 226393.1 239696.1

EP

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

AC C

17225.35 18258.43 22229.48 23838.02 30368.41 34793.37 4733.928 9654.858 10327.82 14489.39 16222.91 20350.89 23395.84 29153.53 32417.97 5478.242 9725.234 12117.9 15821.79 17596.53 21597.66 24736.97 31543.58 35136.17 5347.989 7977.094 10206.26 13233.86 15456.95 20435.66 23594.26 28347.76 30871.78 5743.516 9665.941 12361.27 15997.18 17695.24 21897.01 24183.45 29347.74 32694.54 5449.311 10787.06 12053.15 14923.74 15800.66

RI PT

ACCEPTED MANUSCRIPT

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

286166.1 327696.2 388219.8 452039.2 74314.91 142951.1 197652.6 268687.9 310975.8 374645.1 448248.3

179.7332 200.3137 229.4012 259.1042 61.12155 103.1534 133.6767 170.8961 192.0945 222.9614 257.3645

2427.565 2705.536 3098.406 3499.589 825.5378 1393.241 1805.503 2308.206 2594.523 3011.427 3476.091

AC C

EP

TE D

M AN U

SC

18863.95 21601.59 25591.28 29798.23 4898.807 9423.274 13029.18 17711.79 20499.4 24696.45 29548.34

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

Re

RePR 15.9 14473.49 15.9 76391.51

RI PT

M AN U TE D EP AC C

Pr 5000 40000

SC

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04601731 73.228819 60.5341941 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8333743 114.02112 103.854921 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6091968 145.27525 136.771494 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5438912 184.39553 180.878658 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9080838 216.74782 216.986307 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1383667 241.10514 246.006532 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2960579 247.95851 253.655111 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575419 277.97486 290.119402 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7894632 294.97439 309.411637 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718015 4523.427 42245.56 5.5 15.9 671704.4 0.105

0 550000

0 40000

0 5

1 1

ACCEPTED MANUSCRIPT

Nu_DB 65.30587 111.9013 130.5425 175.1432 172.3848 201.7167 234.2418 264.4811 297.8724

Nu_Gen 52.65631 101.9563 121.436 171.1343 168.0321 201.7188 238.1897 274.8055 314.1761

(Hnf/Hpf)V 1.10476451 1.07797523 1.01117157 1.0026325 1.0162503 1.05518168 1.04139384 1.07324153 1.08373015

M AN U TE D EP

(Hnf/Hpf)Re 1.075865026 1.076560447 1.082089197 1.065081018 1.079320978 1.090168255 1.127583933 1.08016342 1.087367899

RI PT

h_exp-0.05sK Nu_exp-0.05s 996.5051 0.117904 65.07888109 1682.359 0.117007 110.7126768 1891.455 0.114796 126.870515 2509.066 0.115016 167.9756577 2502.653 0.115023 167.5351509 3007.808 0.115881 199.861825 3511.754 0.114451 236.2631742 3969.847 0.116747 261.8304753 4510.361 0.116847 297.2255786

SC

Vel Pr Re^0.8 Pr^0.4 Pe 0.698716 13.9586495 13807.9887 77437.65 1.386518 14.5095547 24215.8436 154778.6 1.73881 16.1181284 30089.3486 197782.3 2.501792 15.937742 40097.8984 283984.9 2.4521 15.9363724 39464.3398 278393.2 2.944027 15.2837703 45035.2234 331804.9 3.632241 16.4055232 54567.068 414396.2 4.077402 14.6907251 57662.4105 456410 4.72499 14.6135602 64737.5239 528148.6

AC C

RE 5547.646 10667.36 12270.8 17818.39 17469.05 21709.62 25259.55 31067.9 36140.99

(Hnf/Hpf)Pe 1.16385706 1.129098234 1.043345026 1.036233883 1.050160357 1.096795616 1.071947184 1.121686405 1.133935255

0.05% 13nm0.05% 13nm0.05% 13nm 1.083228 1.054891 1.141168 1.030881 1.029528 1.079771 0.979 1.047661 1.01015 0.998521 1.060714 1.031985 0.992135 1.053709 1.02524 1.015733 1.049411 1.055791 1.017159 1.101343 1.047001 1.0871 1.094111 1.136171 1.091849 1.095514 1.14243

ACCEPTED MANUSCRIPT

K 0.111858 0.112378 0.110702 0.111413 0.1102 0.111389 0.111076 0.112173 0.111341

Nu_exp-0.5lNu_DB 75.93648 74.21862 112.1558 109.9809 140.3751 138.304 168.7731 166.8019 185.5256 186.3786 224.8539 215.7783 246.1604 233.3266 276.9776 269.4173 316.0861 296.4203

Nu_Gen 61.61831 100.0557 129.9734 162.225 183.2382 217.8415 237.7497 280.8886 311.7457

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe0.05% 50nm0.05% 50nm0.05% 50nm 1.099152 1.099152 1.11 1.05866 1.05866 1.069107784 1.113433 1.113433 1.128392 1.050546 1.050546 1.064659623 1.048862 1.048862 1.050909 1.013903 1.013903 1.015881482 1.071331 1.071331 1.078583 1.042452 1.042452 1.04950811 1.010491 1.010491 1.008793 1.001131 1.001131 0.999448778 1.102514 1.102514 1.109732 1.09573 1.09573 1.102903575 1.104432 1.104432 1.109397 1.126202 1.126202 1.131265382 1.115429 1.115429 1.128802 1.059624 1.059624 1.072328062 1.126469 1.126469 1.133281 1.095379 1.095379 1.102003867

RI PT

h_exp-05l 1103.125 1636.863 2018.149 2442.011 2655.192 3252.765 3550.96 4034.975 4570.553

M AN U

SC

Re^0.8 Pr^0.4 Pe 16196.9517 93294.23935 23464.2506 149681.3739 31871.4236 212550.6416 37151.5957 261122.9317 44053.3846 315206.0235 48115.4826 360595.7866 52801.0675 402532.3488 57990.7295 462121.5199 66256.6455 537361.1463

TE D

Pr 14.71455 14.16976 16.1123 15.22325 16.80809 15.25252 15.63185 14.3803 15.31377

EP

Vel 0.798449 1.286689 1.801282 2.22622 2.659148 3.073434 3.422132 3.9654 4.577204

AC C

RE 6340.269 10563.44 13191.82 17152.91 18753.23 23641.72 25750.78 32135.73 35090.06

ACCEPTED MANUSCRIPT

Nu_exp-0.2sNu_DB 61.4864 56.11831 101.3997 99.65 117.0625 113.4808 144.1866 145.8541 165.7678 163.2296 190.284 187.2735 221.3851 216.3877 265.5391 251.2614 288.2756 278.3376

Nu_Gen 43.53593 89.28494 103.3352 139.4522 158.355 186.1855 218.9646 259.7459 291.0525

(Hnf/Hpf)V 1.275443102 1.170830127 1.122631027 1.106681242 1.109358997 1.144029489 1.127668695 1.180545902 1.141684605

(Hnf/Hpf)Re 1.284093219 1.194488999 1.227873383 1.167623135 1.207360834 1.198318539 1.213244673 1.248157954 1.227576581

RI PT

h_exp-0.2s K 1047.632 0.131196 1714.759 0.130214 1913.001 0.125831 2396.274 0.127968 2714.888 0.126108 3173.68 0.128426 3644.946 0.126775 4407.746 0.127814 4746.987 0.126795

M AN U

SC

Re^0.8 Pr^0.4 Pe 11433.4124 62118.39 20582.3174 128792.6 25193.9201 160907.9 31208.9145 213539.6 36054.3463 252393.2 39768.2765 290018.6 47238.9297 355530.6 53855.0394 422040.8 60702.7119 486622

TE D

Pr 13.12195 13.42481 15.1415 14.239 15.01334 14.05985 14.72286 14.27954 14.69851

EP

Vel 0.621545 1.280633 1.547519 2.087761 2.432977 2.845743 3.444888 4.125298 4.719306

AC C

RE 4733.928 9593.626 10626.95 14996.81 16811.26 20627.44 24148.21 29555.64 33106.89

(Hnf/Hpf)Pe0.2% 13nm0.2% 13nm0.2% 13nm 1.459534 1.201224 1.20937 1.374602 1.333129 1.070038 1.09166 1.218366 1.244615 1.003994 1.098114 1.113087 1.243185 0.99789 1.052841 1.120974 1.232173 0.999596 1.087901 1.110258 1.288856 1.030742 1.079656 1.161228 1.257683 1.033747 1.112196 1.152933 1.325912 1.10662 1.169998 1.242883 1.274226 1.039619 1.117833 1.160312

ACCEPTED MANUSCRIPT

K 0.125829 0.125479 0.121532 0.123265 0.122087 0.123829 0.122335 0.124765 0.123391

Nu_exp-0.2lNu_DB 66.72749 62.98494 111.4692 100.0137 138.1021 128.3917 167.2666 155.0902 186.1079 171.6368 216.0257 196.3328 243.429 224.3843 286.1464 262.6416 310.7312 293.1144

Nu_Gen 50.56447 89.71656 119.5899 149.7068 167.8881 196.5216 228.0024 273.6766 308.9321

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.218923 1.195139 1.348647044 1.27567 1.25802 1.410155626 1.161001 1.237999 1.252011073 1.195828 1.22944 1.303905023 1.180646 1.243792 1.277970146 1.230182 1.250703 1.346278479 1.180497 1.248452 1.279710732 1.234643 1.233206 1.359003846 1.177607 1.207667 1.285088932

RI PT

h_exp-0.2l 1090.419 1816.499 2179.715 2677.686 2950.823 3474.048 3867.521 4636.501 4979.387

SC

Re^0.8 Pr^0.4 Pe 12902.1264 72085.25 20590.1435 129029.1 28553.2441 188025.5 33282.4345 231137 37719.4422 267611.9 41666.9541 307506 49399.4289 374652.4 54765.8073 435952.8 62745.437 511129.2

M AN U

13.241 13.352 15.18486 14.30861 14.8869 14.04574 14.93123 13.63922 14.24912

TE D

Pr

EP

Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561

AC C

RE 5444.095 9663.65 12382.43 16153.7 17976.33 21893.18 25091.86 31963.17 35870.93

0.2% 50nm0.2% 50nm0.2% 50nm 1.176226 1.153275 1.301406 1.193207 1.176698 1.318999 1.072299 1.143413 1.156355 1.109216 1.140394 1.209465 1.072065 1.129403 1.160439 1.117188 1.135824 1.222621 1.099887 1.163201 1.192325 1.151444 1.150105 1.267425 1.096179 1.12416 1.196228

ACCEPTED MANUSCRIPT

Nu_exp-0.3sNu_DB 67.6355 64.03218 102.797 88.42092 126.7817 114.3404 156.1554 137.6449 174.9715 159.5505 222.3501 196.6073 248.0932 223.3202 286.7741 251.8322 314.4038 271.8178

Nu_Gen 51.22818 77.12423 104.0727 130.0495 153.8867 195.9333 226.02 259.8369 282.7461

(Hnf/Hpf)V 1.185641083 1.329027593 1.195267188 1.252527278 1.180590009 1.229592283 1.185193237 1.248724405 1.252069608

M AN U TE D

(Hnf/Hpf)Re 1.254279776 1.374293179 1.332620188 1.353085775 1.31848137 1.355397074 1.340037919 1.359803446 1.388479936

RI PT

h_exp-0.3s K 1130.946 0.128753 1738.584 0.130228 2071.507 0.125812 2585.771 0.127504 2856.874 0.125723 3650.063 0.126402 4031.153 0.125114 4730.886 0.127026 5148.601 0.126093

SC

Pr Re^0.8 Pr^0.4 Pe 14.21163 13685.3757 76235.97 13.65727 18452.0874 111870.6 15.51732 25760.9561 164436.5 14.7233 30049.3645 201972.8 15.55859 36004.1494 249717 15.22936 43800.6874 320760.4 15.87839 51013.3747 384063.8 14.90663 55387.4257 432433.3 15.38466 60926.0106 483316.3

EP

Vel 0.749289 1.112027 1.580575 1.966943 2.398989 3.09715 3.671456 4.201294 4.654405

AC C

RE 5364.338 8191.285 10596.97 13717.9 16050.11 21061.97 24187.83 29009.45 31415.48

(Hnf/Hpf)Pe 1.337506581 1.51288134 1.324554106 1.402612492 1.307718957 1.367532613 1.307640674 1.395690271 1.389587622

0.3% 13nm 0.3% 13nm 0.3% 13nm 1.048587 1.109291 1.182897 1.16447 1.204131 1.32556 1.050256 1.170945 1.163857 1.086559 1.173792 1.216757 1.031577 1.152064 1.14266 1.079922 1.190414 1.201072 1.029352 1.163836 1.135699 1.089969 1.186926 1.218251 1.123628 1.246045 1.247039

ACCEPTED MANUSCRIPT

K 0.102582 0.126427 0.123222 0.124255 0.124042 0.124885 0.124227 0.126915 0.125735

Nu_exp-0.3lNu_DB 85.99118 67.21606 120.1099 102.416 150.6336 132.1555 188.1594 158.9348 188.3668 170.0043 239.7737 202.3768 255.5954 220.067 284.4845 248.5357 312.3335 275.2068

Nu_Gen 54.71687 92.06135 123.5585 153.6267 165.9727 203.0339 223.0541 257.2314 287.9402

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.178051 1.195691 1.306495845 1.32676 1.351873 1.474992721 1.224673 1.340405 1.334858122 1.294313 1.382152 1.420067544 1.207024 1.295278 1.322774477 1.308613 1.377506 1.441560308 1.269144 1.356096 1.392390322 1.304148 1.315634 1.454974513 1.270445 1.312958 1.406691714

RI PT

h_exp-0.3l 1145.606 1972.101 2410.568 3036.336 3034.471 3888.86 4123.626 4689.025 5100.145

M AN U

SC

Re^0.8 Pr^0.4 Pe 14105.5796 79778.58 21516.0126 135176.6 29731.7483 196826.1 34929.1963 243096.3 37532.066 265444.5 43867.2776 325060.5 48387.8929 365279.5 51687.2146 405986.3 58611.4662 470388.7

TE D

Pr 13.78509 13.8103 15.48003 14.88776 15.0009 14.54944 14.89987 13.57908 14.12815

EP

Vel 0.767586 1.304545 1.853157 2.307685 2.51621 3.101358 3.467357 3.935347 4.516705

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

0.3% 50nm0.3% 50nm0.3% 50nm 1.07283 1.088895 1.189802 1.197519 1.220186 1.331312 1.092166 1.195376 1.190429 1.155977 1.234428 1.268291 1.071911 1.150286 1.174704 1.167418 1.228876 1.28602 1.112423 1.188638 1.22045 1.157526 1.167722 1.291397 1.108565 1.145661 1.227452

ACCEPTED MANUSCRIPT

Nu_Gen 52.01392 109.5255 126.9408 149.2917 161.4681 182.3632 209.2581 236.2014 272.1572

(Hnf/Hpf)V 1.370130052 1.296301535 1.283756653 1.324405837 1.289846457 1.346430765 1.318479734 1.353072011 1.340044821

(Hnf/Hpf)Re 1.537441677 1.513339277 1.592212691 1.582594713 1.55742004 1.551848589 1.543975997 1.500626002 1.532098163

(Hnf/Hpf)Pe0.5% 13nm 1.599731 1.489318 1.447077 1.5095 1.465359 1.554578 1.51327 1.589468 1.552256

RI PT

Nu_exp-0.5sNu_DB 79.47883 64.97121 142.8185 119.4484 168.6683 136.156 193.8406 155.8581 203.7651 166.9166 227.138 184.7466 254.3888 208.6477 276.3672 231.0418 319.2169 262.5832

SC

h_exp-0.5s K 1389.448 0.134611 2445.348 0.13184 2818.264 0.128659 3284.955 0.130489 3438.53 0.129937 3912.965 0.13265 4349.012 0.131639 4865.766 0.135567 5521.925 0.133197

M AN U

Re^0.8 Pr^0.4 Pe 14144.63 78838.83 27114.33 174758.2 32807.68 216325.8 36219.19 248522.8 39187.97 273075.1 41381.97 298100.7 47507.67 351834.9 49632.14 380732.8 58319.86 459362

TE D

Pr 14.65539 15.71246 17.3558 16.33912 16.62016 15.36753 15.79295 14.33289 15.15173

EP

Vel 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418

AC C

RE 5379.509 11122.27 12464.18 15210.3 16430.35 19398.08 22277.97 26563.57 30317.47

1.058302489 1.099738065 1.108348345 1.135471921 1.101384653 1.176735755 1.143075549 1.138414644 1.156510411

0.5% 13nm0.5% 13nm 1.187536 1.235649 1.283865 1.263487 1.374658 1.249353 1.356829 1.294162 1.329863 1.251252 1.356264 1.358649 1.338573 1.311951 1.26256 1.337308 1.32226 1.339657

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

RE Vel Pr Re^0.8 Pr^0.4 Pe h_exp-0.5l K Nu_exp-0.5lNu_DB Nu_Gen (Hnf/Hpf)V (Hnf/Hpf)Re (Hnf/Hpf)Pe0.5% 50nm 4922.87805 0.699653673 14.59087644 13117.66821 71829.10536 1284.608568 0.128112 77.2099 60.41373 47.33686322 1.422590845 1.525969862 1.593409 9750.402834 1.369898174 14.33141543 22259.076 139737.0737 2046.873625 0.128373 122.7747 103.6243 93.08967541 1.324207643 1.407418926 1.490866 13180.32319 2.081466016 16.62645037 32865.51092 219141.9895 2971.416699 0.124479 183.8058 139.955 131.5091157 1.375573466 1.605362507 1.51001 18148.94292 2.845290758 16.48304217 42084.13815 299149.7916 3849.468936 0.124687 237.7217 180.1457 176.4150658 1.387762624 1.610164159 1.525059 20828.32383 3.363085294 17.08011992 48687.1522 355750.2688 4210.704877 0.123891 261.7002 204.0082 203.0491413 1.327945304 1.577544977 1.45223 24946.99404 3.911925305 16.48847461 54299.40348 411337.8779 5065.259953 0.124683 312.8139 232.3885 235.9882169 1.415484068 1.64262173 1.555391 29650.52862 4.804751989 17.15686942 64873.00241 508710.2476 5982.985833 0.123804 372.1111 271.0997 280.3462331 1.418393995 1.689827704 1.550024

0.5% 50nm 1.120787317 1.123796049 1.18396894 1.210760282 1.123654624 1.237425533 1.230750039

1.202234411 1.194413758 1.381750515 1.404795588 1.334855963 1.43599078 1.466274899

0.5% 50nm 1.255366 1.265231 1.29968 1.330545 1.228819 1.359733 1.344966

ACCEPTED MANUSCRIPT

1.8

0.5% 50nm 1.7

RI PT

0.5% 13nm 1.6

0.3% 50nm 0.3% 13nm

SC

1.4 1.3

M AN U

Merit Number

1.5

1.2 1.1

0.9

AC C

EP

0

TE D

1

200000

400000

Pe

0.2% 50nm 0.2% 13nm 0.05% 50nm 0.05% 13nm 600000

800000

ACCEPTED MANUSCRIPT

0.80 1.29 1.80 2.23 2.66 3.07 3.42 3.97 4.58 Vel 0.70 1.26 1.56 2.31 2.75 3.18 3.28 4.03 4.73

H 329.594 679.478 1183.04 1636.336 2059.792 2462.359 2849.026 3222.952 3586.306 3940.664 4287.216 4626.894 4960.442 5288.47 5611.485 5929.914 6244.122 888.0548 1536.526 1841.624 2463.771 2424.544 2806.421 3320.008 3641.717 4097.511 #VALUE! 888.0548 1447.366 1894.37 2244.16 2586.982 2904.682 3165.46 3561.468 3994.658 #VALUE! 891.291 1425.054 1690.124 2312.586 2655.211 2981.576 3059.105 3605.963 4104.4

RI PT

Nu 24.17023 50.30751 87.59046 121.1518 152.5038 182.3093 210.9375 238.6224 265.5246 291.7607 317.4189 342.5681 367.2635 391.5502 415.4657 439.0417 462.3052 65.75021 113.762 136.351 182.4138 179.5095 207.7831 245.8083 269.6272 303.3734 #VALUE! 65.75021 107.1607 140.2562 166.1542 191.5361 215.0582 234.3658 263.6856 295.7584 #VALUE! 65.98982 105.5088 125.1342 171.2203 196.5877 220.7513 226.4915 266.9799 303.8835

SC

Pe 23304.19 58260.47 116520.9 174781.4 233041.9 291302.3 349562.8 407823.3 466083.8 524344.2 582604.7 640865.2 699125.6 757386.1 815646.6 873907 932167.5 81415 161558.4 202607.8 291511.2 285721 343040.8 423232.1 475102.7 550560.2 #VALUE! 81415 149926.2 209887.1 259401.3 309846.4 358119.5 398750 462052.1 533340.2 #VALUE! 81786.03 147042.8 181992.3 269325.2 320094.7 370008.8 382074.3 469279.1 551717.6

M AN U

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

TE D

Vel

Re Pr 1536.202 3840.506 7681.011 11521.52 15362.02 19202.53 23043.03 26883.54 30724.04 34564.55 38405.06 42245.56 46086.07 49926.57 53767.08 57607.58 61448.09 5366.843 10649.86 13355.82 19216.29 18834.61 22613.1 27899.28 31318.57 36292.7 #VALUE! 5366.843 9883.071 13835.67 17099.62 20424.94 23607.08 26285.43 30458.28 35157.56 #VALUE! 5391.301 9692.999 11996.86 17753.8 21100.51 24390.82 25186.17 30934.68 36368.99

EP

0.20 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 0.70 1.39 1.74 2.50 2.45 2.94 3.63 4.08 4.72

AC C

V

#VALUE! 948.068 1494.933 1849.591 2302.415 2485.954 2743.895 2933.17 3570.648 3966.328 #VALUE! 808.6815 1441.913 1677.676 2131.788 2409.405 2731.215 3182.288 3675.899 4093.567 #VALUE! 880.739 1401.932 1848.404 2204.555 2460.67 2780.331 3225.505 3697.252 4162.99 939.1149 1287.928 1706.285 2032.511 2382.44 2922.599 3348.653 3729.974 4048.468 957.4169 1463.412 1937.89 2309.62 2475.124 2925.775 3198.882 3539.858

SC

#VALUE! 70.1935 110.6826 136.9409 170.4673 184.0562 203.1538 217.1674 264.3653 293.6608 #VALUE! 59.87353 106.7571 124.2126 157.8343 178.3886 202.215 235.6117 272.1579 303.0814 #VALUE! 65.20856 103.7969 136.853 163.2219 182.1842 205.8514 238.8114 273.7388 308.2214 69.53063 95.35623 126.3307 150.484 176.3922 216.3847 247.9291 276.1615 299.7424 70.88568 108.3488 143.4784 171.0007 183.2544 216.6199 236.8403 262.0856

M AN U

#VALUE! 88349.5 156110.4 203703.9 267845.4 294795.7 333514.1 362515.3 463541.5 528616.3 #VALUE! 72423.01 149220.6 180318.3 243267.8 283492.8 331588.7 401401.6 480683.5 549897.9 #VALUE! 80577.5 144066.6 203540.6 253691.5 291052.6 339059 408227.1 484176.3 561579.8 87307.82 129574.4 184170.1 229190.1 279532.4 360882.9 427801.6 489538.7 542335.7 89439.86 152006.8 215931.6 268893.6 293191.2 361373.2 404019.7 458550.3

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

#VALUE! 5823.962 10290.73 13428.08 17656.26 19432.81 21985.11 23896.86 30556.46 34846.16 #VALUE! 4774.094 9836.557 11886.51 16036.11 18687.72 21858.18 26460.23 31686.46 36249.04 #VALUE! 5311.635 9496.808 13417.31 16723.24 19186.06 22350.63 26910.16 31916.7 37019.1 5755.295 8541.493 12140.41 15108.11 18426.66 23789.25 28200.5 32270.18 35750.54 5895.838 10020.23 14234.12 17725.35 19327.04 23821.57 26632.81 30227.45

AC C

Vel 0.758229 1.339763 1.748217 2.298689 2.52998 2.862267 3.11116 3.978182 4.536663 Vel 0.62 1.28 1.55 2.09 2.43 2.85 3.44 4.13 4.72 Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561 0.75 1.11 1.58 1.97 2.40 3.10 3.67 4.20 4.65 0.77 1.30 1.85 2.31 2.52 3.10 3.47 3.94

RI PT

ACCEPTED MANUSCRIPT

3952.363 998.3795 1857.162 2161.295 2441.875 2624.52 2861.127 3247.374 3540.343 4056.825 889.0085 1521.774 2126.644 2730.868 3121.689 3522.993 4152.754 922.0801 1565.064 1679.369 2249.668 2227.969 2716.355 3066.233 3597.444 4107.391 1048.957 1534.846 1779.974 2223.705 2342.924 2874.383 3095.506 3686.68 3988.522 914.2035 1454.451 1555.335 2199.68 2436.893 2900.474 2917.17 3607.21 3976.339 1004.491 1568.337 1752.876

SC

292.6269 73.91849 137.5014 160.0189 180.7927 194.3154 211.8334 240.4306 262.1216 300.3611 65.82082 112.6698 157.4535 202.1893 231.1251 260.837 307.4635 68.26939 115.875 124.3379 166.562 164.9554 201.1147 227.0192 266.3492 304.1049 77.66317 113.6377 131.7865 164.6397 173.4665 212.8149 229.1865 272.9561 295.304 67.68622 107.6853 115.1546 162.8609 180.4238 214.7467 215.9827 267.0723 294.402 74.371 116.1173 129.7803

M AN U

526290.7 94248.47 204746.7 247484.1 288276.4 315476.6 351419.7 411689.8 458628.9 543735.4 81524.3 159621.8 242534.4 331535.9 391869.9 455821.2 559854.2 85332.71 165317.9 180545.8 260197.3 257064 329335 383187.4 467893.8 552220.2 100254 161337.7 194165.4 256449.1 273749 353456.2 387765.5 482446.4 532316.2 84422.53 150844.2 164034.4 252990.5 287541.3 357471.2 360045 469482.1 530284.5 94970.23 165750.2 190477.5

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

34692.86 6212.82 13496.81 16314.04 19003.06 20796.08 23165.44 27138.42 30232.63 35842.8 5374.048 10522.2 15987.76 21854.71 25831.9 30047.54 36905.35 5625.096 10897.69 11901.5 17152.1 16945.55 21709.62 25259.55 30843.37 36402.12 6608.704 10635.31 12799.3 16905.02 18045.42 23299.68 25561.34 31802.66 35090.06 5565.097 9943.588 10813.08 16677.03 18954.6 23564.35 23734.02 30948.06 34956.13 6260.398 10926.18 12556.2

AC C

4.52 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418 0.70 1.37 2.08 2.85 3.36 3.91 4.80

RI PT

ACCEPTED MANUSCRIPT

SC

2257.352 2365.024 2768.268 2927.392 3553.058 3961.52 803.2339 1420.566 1499.242 1965.644 2151.631 2579.476 2883.869 3438.884 3743.633 902.7711 1428.844 1703.752 2108.964 2296.182 2705.142 3015.379 3662.634 3992.714 885.5582 1219.384 1485.108 1828.159 2069.969 2588.067 2903.419 3362.635 3600.096 937.577 1421.87 1731.072 2127.646 2306.481 2735.096 2961.279 3457.199 3769.163 898.955 1552.341 1696.466 2012.643 2106.711

M AN U

167.1308 175.1027 204.9583 216.7396 263.0629 293.3049 59.4702 105.1765 111.0015 145.5332 159.3034 190.9804 213.5173 254.6097 277.1729 66.83978 105.7894 126.1432 156.1444 170.0058 200.2846 223.254 271.1758 295.6144 65.56537 90.28131 109.9551 135.3541 153.2573 191.6165 214.9647 248.9643 266.5456 69.41676 105.2731 128.1659 157.5277 170.7683 202.5023 219.2485 255.9657 279.063 66.55724 114.9329 125.6037 149.013 155.9776

TE D

261308.6 276980.4 337221.2 361622.8 460688.7 527815.4 71813.69 146464.2 156673 219804.1 246101.6 308723.1 354914.9 442259 491780.6 83104.93 147531.8 183828.5 240016.5 266939.4 327636.5 375259.8 478516.1 533015.7 81129 121012.5 154829 200757.6 234482 310008.9 357924.9 430035.5 468325 87129.13 146632.3 187520.5 242677.2 268436.8 332177.6 366862.9 445205.2 495976.2 82666.04 163639.6 182846.3 226393.1 239696.1

EP

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

AC C

17225.35 18258.43 22229.48 23838.02 30368.41 34793.37 4733.928 9654.858 10327.82 14489.39 16222.91 20350.89 23395.84 29153.53 32417.97 5478.242 9725.234 12117.9 15821.79 17596.53 21597.66 24736.97 31543.58 35136.17 5347.989 7977.094 10206.26 13233.86 15456.95 20435.66 23594.26 28347.76 30871.78 5743.516 9665.941 12361.27 15997.18 17695.24 21897.01 24183.45 29347.74 32694.54 5449.311 10787.06 12053.15 14923.74 15800.66

RI PT

ACCEPTED MANUSCRIPT

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

286166.1 327696.2 388219.8 452039.2 74314.91 142951.1 197652.6 268687.9 310975.8 374645.1 448248.3

179.7332 200.3137 229.4012 259.1042 61.12155 103.1534 133.6767 170.8961 192.0945 222.9614 257.3645

2427.565 2705.536 3098.406 3499.589 825.5378 1393.241 1805.503 2308.206 2594.523 3011.427 3476.091

AC C

EP

TE D

M AN U

SC

18863.95 21601.59 25591.28 29798.23 4898.807 9423.274 13029.18 17711.79 20499.4 24696.45 29548.34

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

Re

RePR 15.9 14473.49 15.9 76391.51

RI PT

M AN U TE D EP AC C

Pr 5000 40000

SC

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04601731 73.228819 60.5341941 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8333743 114.02112 103.854921 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6091968 145.27525 136.771494 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5438912 184.39553 180.878658 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9080838 216.74782 216.986307 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1383667 241.10514 246.006532 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2960579 247.95851 253.655111 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575419 277.97486 290.119402 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7894632 294.97439 309.411637 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718015 4523.427 42245.56 5.5 15.9 671704.4 0.105

0 550000

0 40000

0 5

1 1

ACCEPTED MANUSCRIPT

Nu_DB 65.30587 111.9013 130.5425 175.1432 172.3848 201.7167 234.2418 264.4811 297.8724

Nu_Gen 52.65631 101.9563 121.436 171.1343 168.0321 201.7188 238.1897 274.8055 314.1761

(Hnf/Hpf)V 1.10476451 1.07797523 1.01117157 1.0026325 1.0162503 1.05518168 1.04139384 1.07324153 1.08373015

M AN U TE D EP

(Hnf/Hpf)Re 1.075865026 1.076560447 1.082089197 1.065081018 1.079320978 1.090168255 1.127583933 1.08016342 1.087367899

RI PT

h_exp-0.05sK Nu_exp-0.05s 996.5051 0.117904 65.07888109 1682.359 0.117007 110.7126768 1891.455 0.114796 126.870515 2509.066 0.115016 167.9756577 2502.653 0.115023 167.5351509 3007.808 0.115881 199.861825 3511.754 0.114451 236.2631742 3969.847 0.116747 261.8304753 4510.361 0.116847 297.2255786

SC

Vel Pr Re^0.8 Pr^0.4 Pe 0.698716 13.9586495 13807.9887 77437.65 1.386518 14.5095547 24215.8436 154778.6 1.73881 16.1181284 30089.3486 197782.3 2.501792 15.937742 40097.8984 283984.9 2.4521 15.9363724 39464.3398 278393.2 2.944027 15.2837703 45035.2234 331804.9 3.632241 16.4055232 54567.068 414396.2 4.077402 14.6907251 57662.4105 456410 4.72499 14.6135602 64737.5239 528148.6

AC C

RE 5547.646 10667.36 12270.8 17818.39 17469.05 21709.62 25259.55 31067.9 36140.99

(Hnf/Hpf)Pe 1.16385706 1.129098234 1.043345026 1.036233883 1.050160357 1.096795616 1.071947184 1.121686405 1.133935255

0.05% 13nm0.05% 13nm0.05% 13nm 1.083228 1.054891 1.141168 1.030881 1.029528 1.079771 0.979 1.047661 1.01015 0.998521 1.060714 1.031985 0.992135 1.053709 1.02524 1.015733 1.049411 1.055791 1.017159 1.101343 1.047001 1.0871 1.094111 1.136171 1.091849 1.095514 1.14243

ACCEPTED MANUSCRIPT

K 0.111858 0.112378 0.110702 0.111413 0.1102 0.111389 0.111076 0.112173 0.111341

Nu_exp-0.5lNu_DB 75.93648 74.21862 112.1558 109.9809 140.3751 138.304 168.7731 166.8019 185.5256 186.3786 224.8539 215.7783 246.1604 233.3266 276.9776 269.4173 316.0861 296.4203

Nu_Gen 61.61831 100.0557 129.9734 162.225 183.2382 217.8415 237.7497 280.8886 311.7457

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe0.05% 50nm0.05% 50nm0.05% 50nm 1.099152 1.099152 1.11 1.05866 1.05866 1.069107784 1.113433 1.113433 1.128392 1.050546 1.050546 1.064659623 1.048862 1.048862 1.050909 1.013903 1.013903 1.015881482 1.071331 1.071331 1.078583 1.042452 1.042452 1.04950811 1.010491 1.010491 1.008793 1.001131 1.001131 0.999448778 1.102514 1.102514 1.109732 1.09573 1.09573 1.102903575 1.104432 1.104432 1.109397 1.126202 1.126202 1.131265382 1.115429 1.115429 1.128802 1.059624 1.059624 1.072328062 1.126469 1.126469 1.133281 1.095379 1.095379 1.102003867

RI PT

h_exp-05l 1103.125 1636.863 2018.149 2442.011 2655.192 3252.765 3550.96 4034.975 4570.553

M AN U

SC

Re^0.8 Pr^0.4 Pe 16196.9517 93294.23935 23464.2506 149681.3739 31871.4236 212550.6416 37151.5957 261122.9317 44053.3846 315206.0235 48115.4826 360595.7866 52801.0675 402532.3488 57990.7295 462121.5199 66256.6455 537361.1463

TE D

Pr 14.71455 14.16976 16.1123 15.22325 16.80809 15.25252 15.63185 14.3803 15.31377

EP

Vel 0.798449 1.286689 1.801282 2.22622 2.659148 3.073434 3.422132 3.9654 4.577204

AC C

RE 6340.269 10563.44 13191.82 17152.91 18753.23 23641.72 25750.78 32135.73 35090.06

ACCEPTED MANUSCRIPT

Nu_exp-0.2sNu_DB 61.4864 56.11831 101.3997 99.65 117.0625 113.4808 144.1866 145.8541 165.7678 163.2296 190.284 187.2735 221.3851 216.3877 265.5391 251.2614 288.2756 278.3376

Nu_Gen 43.53593 89.28494 103.3352 139.4522 158.355 186.1855 218.9646 259.7459 291.0525

(Hnf/Hpf)V 1.275443102 1.170830127 1.122631027 1.106681242 1.109358997 1.144029489 1.127668695 1.180545902 1.141684605

(Hnf/Hpf)Re 1.284093219 1.194488999 1.227873383 1.167623135 1.207360834 1.198318539 1.213244673 1.248157954 1.227576581

RI PT

h_exp-0.2s K 1047.632 0.131196 1714.759 0.130214 1913.001 0.125831 2396.274 0.127968 2714.888 0.126108 3173.68 0.128426 3644.946 0.126775 4407.746 0.127814 4746.987 0.126795

M AN U

SC

Re^0.8 Pr^0.4 Pe 11433.4124 62118.39 20582.3174 128792.6 25193.9201 160907.9 31208.9145 213539.6 36054.3463 252393.2 39768.2765 290018.6 47238.9297 355530.6 53855.0394 422040.8 60702.7119 486622

TE D

Pr 13.12195 13.42481 15.1415 14.239 15.01334 14.05985 14.72286 14.27954 14.69851

EP

Vel 0.621545 1.280633 1.547519 2.087761 2.432977 2.845743 3.444888 4.125298 4.719306

AC C

RE 4733.928 9593.626 10626.95 14996.81 16811.26 20627.44 24148.21 29555.64 33106.89

(Hnf/Hpf)Pe0.2% 13nm0.2% 13nm0.2% 13nm 1.459534 1.201224 1.20937 1.374602 1.333129 1.070038 1.09166 1.218366 1.244615 1.003994 1.098114 1.113087 1.243185 0.99789 1.052841 1.120974 1.232173 0.999596 1.087901 1.110258 1.288856 1.030742 1.079656 1.161228 1.257683 1.033747 1.112196 1.152933 1.325912 1.10662 1.169998 1.242883 1.274226 1.039619 1.117833 1.160312

ACCEPTED MANUSCRIPT

K 0.125829 0.125479 0.121532 0.123265 0.122087 0.123829 0.122335 0.124765 0.123391

Nu_exp-0.2lNu_DB 66.72749 62.98494 111.4692 100.0137 138.1021 128.3917 167.2666 155.0902 186.1079 171.6368 216.0257 196.3328 243.429 224.3843 286.1464 262.6416 310.7312 293.1144

Nu_Gen 50.56447 89.71656 119.5899 149.7068 167.8881 196.5216 228.0024 273.6766 308.9321

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.218923 1.195139 1.348647044 1.27567 1.25802 1.410155626 1.161001 1.237999 1.252011073 1.195828 1.22944 1.303905023 1.180646 1.243792 1.277970146 1.230182 1.250703 1.346278479 1.180497 1.248452 1.279710732 1.234643 1.233206 1.359003846 1.177607 1.207667 1.285088932

RI PT

h_exp-0.2l 1090.419 1816.499 2179.715 2677.686 2950.823 3474.048 3867.521 4636.501 4979.387

SC

Re^0.8 Pr^0.4 Pe 12902.1264 72085.25 20590.1435 129029.1 28553.2441 188025.5 33282.4345 231137 37719.4422 267611.9 41666.9541 307506 49399.4289 374652.4 54765.8073 435952.8 62745.437 511129.2

M AN U

13.241 13.352 15.18486 14.30861 14.8869 14.04574 14.93123 13.63922 14.24912

TE D

Pr

EP

Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561

AC C

RE 5444.095 9663.65 12382.43 16153.7 17976.33 21893.18 25091.86 31963.17 35870.93

0.2% 50nm0.2% 50nm0.2% 50nm 1.176226 1.153275 1.301406 1.193207 1.176698 1.318999 1.072299 1.143413 1.156355 1.109216 1.140394 1.209465 1.072065 1.129403 1.160439 1.117188 1.135824 1.222621 1.099887 1.163201 1.192325 1.151444 1.150105 1.267425 1.096179 1.12416 1.196228

ACCEPTED MANUSCRIPT

Nu_exp-0.3sNu_DB 67.6355 64.03218 102.797 88.42092 126.7817 114.3404 156.1554 137.6449 174.9715 159.5505 222.3501 196.6073 248.0932 223.3202 286.7741 251.8322 314.4038 271.8178

Nu_Gen 51.22818 77.12423 104.0727 130.0495 153.8867 195.9333 226.02 259.8369 282.7461

(Hnf/Hpf)V 1.185641083 1.329027593 1.195267188 1.252527278 1.180590009 1.229592283 1.185193237 1.248724405 1.252069608

M AN U TE D

(Hnf/Hpf)Re 1.254279776 1.374293179 1.332620188 1.353085775 1.31848137 1.355397074 1.340037919 1.359803446 1.388479936

RI PT

h_exp-0.3s K 1130.946 0.128753 1738.584 0.130228 2071.507 0.125812 2585.771 0.127504 2856.874 0.125723 3650.063 0.126402 4031.153 0.125114 4730.886 0.127026 5148.601 0.126093

SC

Pr Re^0.8 Pr^0.4 Pe 14.21163 13685.3757 76235.97 13.65727 18452.0874 111870.6 15.51732 25760.9561 164436.5 14.7233 30049.3645 201972.8 15.55859 36004.1494 249717 15.22936 43800.6874 320760.4 15.87839 51013.3747 384063.8 14.90663 55387.4257 432433.3 15.38466 60926.0106 483316.3

EP

Vel 0.749289 1.112027 1.580575 1.966943 2.398989 3.09715 3.671456 4.201294 4.654405

AC C

RE 5364.338 8191.285 10596.97 13717.9 16050.11 21061.97 24187.83 29009.45 31415.48

(Hnf/Hpf)Pe 1.337506581 1.51288134 1.324554106 1.402612492 1.307718957 1.367532613 1.307640674 1.395690271 1.389587622

0.3% 13nm 0.3% 13nm 0.3% 13nm 1.048587 1.109291 1.182897 1.16447 1.204131 1.32556 1.050256 1.170945 1.163857 1.086559 1.173792 1.216757 1.031577 1.152064 1.14266 1.079922 1.190414 1.201072 1.029352 1.163836 1.135699 1.089969 1.186926 1.218251 1.123628 1.246045 1.247039

ACCEPTED MANUSCRIPT

K 0.102582 0.126427 0.123222 0.124255 0.124042 0.124885 0.124227 0.126915 0.125735

Nu_exp-0.3lNu_DB 85.99118 67.21606 120.1099 102.416 150.6336 132.1555 188.1594 158.9348 188.3668 170.0043 239.7737 202.3768 255.5954 220.067 284.4845 248.5357 312.3335 275.2068

Nu_Gen 54.71687 92.06135 123.5585 153.6267 165.9727 203.0339 223.0541 257.2314 287.9402

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.178051 1.195691 1.306495845 1.32676 1.351873 1.474992721 1.224673 1.340405 1.334858122 1.294313 1.382152 1.420067544 1.207024 1.295278 1.322774477 1.308613 1.377506 1.441560308 1.269144 1.356096 1.392390322 1.304148 1.315634 1.454974513 1.270445 1.312958 1.406691714

RI PT

h_exp-0.3l 1145.606 1972.101 2410.568 3036.336 3034.471 3888.86 4123.626 4689.025 5100.145

M AN U

SC

Re^0.8 Pr^0.4 Pe 14105.5796 79778.58 21516.0126 135176.6 29731.7483 196826.1 34929.1963 243096.3 37532.066 265444.5 43867.2776 325060.5 48387.8929 365279.5 51687.2146 405986.3 58611.4662 470388.7

TE D

Pr 13.78509 13.8103 15.48003 14.88776 15.0009 14.54944 14.89987 13.57908 14.12815

EP

Vel 0.767586 1.304545 1.853157 2.307685 2.51621 3.101358 3.467357 3.935347 4.516705

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

0.3% 50nm0.3% 50nm0.3% 50nm 1.07283 1.088895 1.189802 1.197519 1.220186 1.331312 1.092166 1.195376 1.190429 1.155977 1.234428 1.268291 1.071911 1.150286 1.174704 1.167418 1.228876 1.28602 1.112423 1.188638 1.22045 1.157526 1.167722 1.291397 1.108565 1.145661 1.227452

ACCEPTED MANUSCRIPT

Nu_Gen 52.01392 109.5255 126.9408 149.2917 161.4681 182.3632 209.2581 236.2014 272.1572

(Hnf/Hpf)V 1.370130052 1.296301535 1.283756653 1.324405837 1.289846457 1.346430765 1.318479734 1.353072011 1.340044821

(Hnf/Hpf)Re 1.537441677 1.513339277 1.592212691 1.582594713 1.55742004 1.551848589 1.543975997 1.500626002 1.532098163

(Hnf/Hpf)Pe0.5% 13nm 1.599731 1.489318 1.447077 1.5095 1.465359 1.554578 1.51327 1.589468 1.552256

RI PT

Nu_exp-0.5sNu_DB 79.47883 64.97121 142.8185 119.4484 168.6683 136.156 193.8406 155.8581 203.7651 166.9166 227.138 184.7466 254.3888 208.6477 276.3672 231.0418 319.2169 262.5832

SC

h_exp-0.5s K 1389.448 0.134611 2445.348 0.13184 2818.264 0.128659 3284.955 0.130489 3438.53 0.129937 3912.965 0.13265 4349.012 0.131639 4865.766 0.135567 5521.925 0.133197

M AN U

Re^0.8 Pr^0.4 Pe 14144.63 78838.83 27114.33 174758.2 32807.68 216325.8 36219.19 248522.8 39187.97 273075.1 41381.97 298100.7 47507.67 351834.9 49632.14 380732.8 58319.86 459362

TE D

Pr 14.65539 15.71246 17.3558 16.33912 16.62016 15.36753 15.79295 14.33289 15.15173

EP

Vel 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418

AC C

RE 5379.509 11122.27 12464.18 15210.3 16430.35 19398.08 22277.97 26563.57 30317.47

1.058302489 1.099738065 1.108348345 1.135471921 1.101384653 1.176735755 1.143075549 1.138414644 1.156510411

0.5% 13nm0.5% 13nm 1.187536 1.235649 1.283865 1.263487 1.374658 1.249353 1.356829 1.294162 1.329863 1.251252 1.356264 1.358649 1.338573 1.311951 1.26256 1.337308 1.32226 1.339657

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

RE Vel Pr Re^0.8 Pr^0.4 Pe h_exp-0.5l K Nu_exp-0.5lNu_DB Nu_Gen (Hnf/Hpf)V (Hnf/Hpf)Re (Hnf/Hpf)Pe0.5% 50nm 4922.87805 0.699653673 14.59087644 13117.66821 71829.10536 1284.608568 0.128112 77.2099 60.41373 47.33686322 1.422590845 1.525969862 1.593409 9750.402834 1.369898174 14.33141543 22259.076 139737.0737 2046.873625 0.128373 122.7747 103.6243 93.08967541 1.324207643 1.407418926 1.490866 13180.32319 2.081466016 16.62645037 32865.51092 219141.9895 2971.416699 0.124479 183.8058 139.955 131.5091157 1.375573466 1.605362507 1.51001 18148.94292 2.845290758 16.48304217 42084.13815 299149.7916 3849.468936 0.124687 237.7217 180.1457 176.4150658 1.387762624 1.610164159 1.525059 20828.32383 3.363085294 17.08011992 48687.1522 355750.2688 4210.704877 0.123891 261.7002 204.0082 203.0491413 1.327945304 1.577544977 1.45223 24946.99404 3.911925305 16.48847461 54299.40348 411337.8779 5065.259953 0.124683 312.8139 232.3885 235.9882169 1.415484068 1.64262173 1.555391 29650.52862 4.804751989 17.15686942 64873.00241 508710.2476 5982.985833 0.123804 372.1111 271.0997 280.3462331 1.418393995 1.689827704 1.550024

0.5% 50nm 1.120787317 1.123796049 1.18396894 1.210760282 1.123654624 1.237425533 1.230750039

1.202234411 1.194413758 1.381750515 1.404795588 1.334855963 1.43599078 1.466274899

0.5% 50nm 1.255366 1.265231 1.29968 1.330545 1.228819 1.359733 1.344966

ACCEPTED MANUSCRIPT

1.8

0.5% 50nm 1.7

RI PT

0.5% 13nm

1.6

0.3% 50nm 0.3% 13nm

SC

1.4 1.3

0.2% 50nm

M AN U

Merit Number

1.5

1.2 1.1

0.9

AC C

EP

0

TE D

1

2

0.2% 13nm 0.05% 50nm 0.05% 13nm

4

u (m/s)

6

8

ACCEPTED MANUSCRIPT

Re

RePR 15.9 14473.49 15.9 76391.51

RI PT

M AN U TE D EP AC C

Pr 5000 40000

SC

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04601731 73.228819 60.5341941 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8333743 114.02112 103.854921 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6091968 145.27525 136.771494 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5438912 184.39553 180.878658 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9080838 216.74782 216.986307 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1383667 241.10514 246.006532 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2960579 247.95851 253.655111 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575419 277.97486 290.119402 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7894632 294.97439 309.411637 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718015 4523.427 42245.56 5.5 15.9 671704.4 0.105

0 550000

0 40000

0 5

1 1

ACCEPTED MANUSCRIPT

Nu_DB 65.30587 111.9013 130.5425 175.1432 172.3848 201.7167 234.2418 264.4811 297.8724

Nu_Gen 52.65631 101.9563 121.436 171.1343 168.0321 201.7188 238.1897 274.8055 314.1761

(Hnf/Hpf)V 1.10476451 1.07797523 1.01117157 1.0026325 1.0162503 1.05518168 1.04139384 1.07324153 1.08373015

M AN U TE D EP

(Hnf/Hpf)Re 1.075865026 1.076560447 1.082089197 1.065081018 1.079320978 1.090168255 1.127583933 1.08016342 1.087367899

RI PT

h_exp-0.05sK Nu_exp-0.05s 996.5051 0.117904 65.07888109 1682.359 0.117007 110.7126768 1891.455 0.114796 126.870515 2509.066 0.115016 167.9756577 2502.653 0.115023 167.5351509 3007.808 0.115881 199.861825 3511.754 0.114451 236.2631742 3969.847 0.116747 261.8304753 4510.361 0.116847 297.2255786

SC

Vel Pr Re^0.8 Pr^0.4 Pe 0.698716 13.9586495 13807.9887 77437.65 1.386518 14.5095547 24215.8436 154778.6 1.73881 16.1181284 30089.3486 197782.3 2.501792 15.937742 40097.8984 283984.9 2.4521 15.9363724 39464.3398 278393.2 2.944027 15.2837703 45035.2234 331804.9 3.632241 16.4055232 54567.068 414396.2 4.077402 14.6907251 57662.4105 456410 4.72499 14.6135602 64737.5239 528148.6

AC C

RE 5547.646 10667.36 12270.8 17818.39 17469.05 21709.62 25259.55 31067.9 36140.99

(Hnf/Hpf)Pe 1.16385706 1.129098234 1.043345026 1.036233883 1.050160357 1.096795616 1.071947184 1.121686405 1.133935255

0.05% 13nm0.05% 13nm0.05% 13nm 1.083228 1.054891 1.141168 1.030881 1.029528 1.079771 0.979 1.047661 1.01015 0.998521 1.060714 1.031985 0.992135 1.053709 1.02524 1.015733 1.049411 1.055791 1.017159 1.101343 1.047001 1.0871 1.094111 1.136171 1.091849 1.095514 1.14243

ACCEPTED MANUSCRIPT

K 0.111858 0.112378 0.110702 0.111413 0.1102 0.111389 0.111076 0.112173 0.111341

Nu_exp-0.5lNu_DB 75.93648 74.21862 112.1558 109.9809 140.3751 138.304 168.7731 166.8019 185.5256 186.3786 224.8539 215.7783 246.1604 233.3266 276.9776 269.4173 316.0861 296.4203

Nu_Gen 61.61831 100.0557 129.9734 162.225 183.2382 217.8415 237.7497 280.8886 311.7457

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe0.05% 50nm0.05% 50nm0.05% 50nm 1.099152 1.099152 1.11 1.05866 1.05866 1.069107784 1.113433 1.113433 1.128392 1.050546 1.050546 1.064659623 1.048862 1.048862 1.050909 1.013903 1.013903 1.015881482 1.071331 1.071331 1.078583 1.042452 1.042452 1.04950811 1.010491 1.010491 1.008793 1.001131 1.001131 0.999448778 1.102514 1.102514 1.109732 1.09573 1.09573 1.102903575 1.104432 1.104432 1.109397 1.126202 1.126202 1.131265382 1.115429 1.115429 1.128802 1.059624 1.059624 1.072328062 1.126469 1.126469 1.133281 1.095379 1.095379 1.102003867

RI PT

h_exp-05l 1103.125 1636.863 2018.149 2442.011 2655.192 3252.765 3550.96 4034.975 4570.553

M AN U

SC

Re^0.8 Pr^0.4 Pe 16196.9517 93294.23935 23464.2506 149681.3739 31871.4236 212550.6416 37151.5957 261122.9317 44053.3846 315206.0235 48115.4826 360595.7866 52801.0675 402532.3488 57990.7295 462121.5199 66256.6455 537361.1463

TE D

Pr 14.71455 14.16976 16.1123 15.22325 16.80809 15.25252 15.63185 14.3803 15.31377

EP

Vel 0.798449 1.286689 1.801282 2.22622 2.659148 3.073434 3.422132 3.9654 4.577204

AC C

RE 6340.269 10563.44 13191.82 17152.91 18753.23 23641.72 25750.78 32135.73 35090.06

ACCEPTED MANUSCRIPT

Nu_exp-0.2sNu_DB 61.4864 56.11831 101.3997 99.65 117.0625 113.4808 144.1866 145.8541 165.7678 163.2296 190.284 187.2735 221.3851 216.3877 265.5391 251.2614 288.2756 278.3376

Nu_Gen 43.53593 89.28494 103.3352 139.4522 158.355 186.1855 218.9646 259.7459 291.0525

(Hnf/Hpf)V 1.275443102 1.170830127 1.122631027 1.106681242 1.109358997 1.144029489 1.127668695 1.180545902 1.141684605

(Hnf/Hpf)Re 1.284093219 1.194488999 1.227873383 1.167623135 1.207360834 1.198318539 1.213244673 1.248157954 1.227576581

RI PT

h_exp-0.2s K 1047.632 0.131196 1714.759 0.130214 1913.001 0.125831 2396.274 0.127968 2714.888 0.126108 3173.68 0.128426 3644.946 0.126775 4407.746 0.127814 4746.987 0.126795

M AN U

SC

Re^0.8 Pr^0.4 Pe 11433.4124 62118.39 20582.3174 128792.6 25193.9201 160907.9 31208.9145 213539.6 36054.3463 252393.2 39768.2765 290018.6 47238.9297 355530.6 53855.0394 422040.8 60702.7119 486622

TE D

Pr 13.12195 13.42481 15.1415 14.239 15.01334 14.05985 14.72286 14.27954 14.69851

EP

Vel 0.621545 1.280633 1.547519 2.087761 2.432977 2.845743 3.444888 4.125298 4.719306

AC C

RE 4733.928 9593.626 10626.95 14996.81 16811.26 20627.44 24148.21 29555.64 33106.89

(Hnf/Hpf)Pe0.2% 13nm0.2% 13nm0.2% 13nm 1.459534 1.201224 1.20937 1.374602 1.333129 1.070038 1.09166 1.218366 1.244615 1.003994 1.098114 1.113087 1.243185 0.99789 1.052841 1.120974 1.232173 0.999596 1.087901 1.110258 1.288856 1.030742 1.079656 1.161228 1.257683 1.033747 1.112196 1.152933 1.325912 1.10662 1.169998 1.242883 1.274226 1.039619 1.117833 1.160312

ACCEPTED MANUSCRIPT

K 0.125829 0.125479 0.121532 0.123265 0.122087 0.123829 0.122335 0.124765 0.123391

Nu_exp-0.2lNu_DB 66.72749 62.98494 111.4692 100.0137 138.1021 128.3917 167.2666 155.0902 186.1079 171.6368 216.0257 196.3328 243.429 224.3843 286.1464 262.6416 310.7312 293.1144

Nu_Gen 50.56447 89.71656 119.5899 149.7068 167.8881 196.5216 228.0024 273.6766 308.9321

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.218923 1.195139 1.348647044 1.27567 1.25802 1.410155626 1.161001 1.237999 1.252011073 1.195828 1.22944 1.303905023 1.180646 1.243792 1.277970146 1.230182 1.250703 1.346278479 1.180497 1.248452 1.279710732 1.234643 1.233206 1.359003846 1.177607 1.207667 1.285088932

RI PT

h_exp-0.2l 1090.419 1816.499 2179.715 2677.686 2950.823 3474.048 3867.521 4636.501 4979.387

SC

Re^0.8 Pr^0.4 Pe 12902.1264 72085.25 20590.1435 129029.1 28553.2441 188025.5 33282.4345 231137 37719.4422 267611.9 41666.9541 307506 49399.4289 374652.4 54765.8073 435952.8 62745.437 511129.2

M AN U

13.241 13.352 15.18486 14.30861 14.8869 14.04574 14.93123 13.63922 14.24912

TE D

Pr

EP

Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561

AC C

RE 5444.095 9663.65 12382.43 16153.7 17976.33 21893.18 25091.86 31963.17 35870.93

0.2% 50nm0.2% 50nm0.2% 50nm 1.176226 1.153275 1.301406 1.193207 1.176698 1.318999 1.072299 1.143413 1.156355 1.109216 1.140394 1.209465 1.072065 1.129403 1.160439 1.117188 1.135824 1.222621 1.099887 1.163201 1.192325 1.151444 1.150105 1.267425 1.096179 1.12416 1.196228

ACCEPTED MANUSCRIPT

Nu_exp-0.3sNu_DB 67.6355 64.03218 102.797 88.42092 126.7817 114.3404 156.1554 137.6449 174.9715 159.5505 222.3501 196.6073 248.0932 223.3202 286.7741 251.8322 314.4038 271.8178

Nu_Gen 51.22818 77.12423 104.0727 130.0495 153.8867 195.9333 226.02 259.8369 282.7461

(Hnf/Hpf)V 1.185641083 1.329027593 1.195267188 1.252527278 1.180590009 1.229592283 1.185193237 1.248724405 1.252069608

M AN U TE D

(Hnf/Hpf)Re 1.254279776 1.374293179 1.332620188 1.353085775 1.31848137 1.355397074 1.340037919 1.359803446 1.388479936

RI PT

h_exp-0.3s K 1130.946 0.128753 1738.584 0.130228 2071.507 0.125812 2585.771 0.127504 2856.874 0.125723 3650.063 0.126402 4031.153 0.125114 4730.886 0.127026 5148.601 0.126093

SC

Pr Re^0.8 Pr^0.4 Pe 14.21163 13685.3757 76235.97 13.65727 18452.0874 111870.6 15.51732 25760.9561 164436.5 14.7233 30049.3645 201972.8 15.55859 36004.1494 249717 15.22936 43800.6874 320760.4 15.87839 51013.3747 384063.8 14.90663 55387.4257 432433.3 15.38466 60926.0106 483316.3

EP

Vel 0.749289 1.112027 1.580575 1.966943 2.398989 3.09715 3.671456 4.201294 4.654405

AC C

RE 5364.338 8191.285 10596.97 13717.9 16050.11 21061.97 24187.83 29009.45 31415.48

(Hnf/Hpf)Pe 1.337506581 1.51288134 1.324554106 1.402612492 1.307718957 1.367532613 1.307640674 1.395690271 1.389587622

0.3% 13nm 0.3% 13nm 0.3% 13nm 1.048587 1.109291 1.182897 1.16447 1.204131 1.32556 1.050256 1.170945 1.163857 1.086559 1.173792 1.216757 1.031577 1.152064 1.14266 1.079922 1.190414 1.201072 1.029352 1.163836 1.135699 1.089969 1.186926 1.218251 1.123628 1.246045 1.247039

ACCEPTED MANUSCRIPT

K 0.102582 0.126427 0.123222 0.124255 0.124042 0.124885 0.124227 0.126915 0.125735

Nu_exp-0.3lNu_DB 85.99118 67.21606 120.1099 102.416 150.6336 132.1555 188.1594 158.9348 188.3668 170.0043 239.7737 202.3768 255.5954 220.067 284.4845 248.5357 312.3335 275.2068

Nu_Gen 54.71687 92.06135 123.5585 153.6267 165.9727 203.0339 223.0541 257.2314 287.9402

(Hnf/Hpf)V (Hnf/Hpf)Re(Hnf/Hpf)Pe 1.178051 1.195691 1.306495845 1.32676 1.351873 1.474992721 1.224673 1.340405 1.334858122 1.294313 1.382152 1.420067544 1.207024 1.295278 1.322774477 1.308613 1.377506 1.441560308 1.269144 1.356096 1.392390322 1.304148 1.315634 1.454974513 1.270445 1.312958 1.406691714

RI PT

h_exp-0.3l 1145.606 1972.101 2410.568 3036.336 3034.471 3888.86 4123.626 4689.025 5100.145

M AN U

SC

Re^0.8 Pr^0.4 Pe 14105.5796 79778.58 21516.0126 135176.6 29731.7483 196826.1 34929.1963 243096.3 37532.066 265444.5 43867.2776 325060.5 48387.8929 365279.5 51687.2146 405986.3 58611.4662 470388.7

TE D

Pr 13.78509 13.8103 15.48003 14.88776 15.0009 14.54944 14.89987 13.57908 14.12815

EP

Vel 0.767586 1.304545 1.853157 2.307685 2.51621 3.101358 3.467357 3.935347 4.516705

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

0.3% 50nm0.3% 50nm0.3% 50nm 1.07283 1.088895 1.189802 1.197519 1.220186 1.331312 1.092166 1.195376 1.190429 1.155977 1.234428 1.268291 1.071911 1.150286 1.174704 1.167418 1.228876 1.28602 1.112423 1.188638 1.22045 1.157526 1.167722 1.291397 1.108565 1.145661 1.227452

ACCEPTED MANUSCRIPT

Nu_Gen 52.01392 109.5255 126.9408 149.2917 161.4681 182.3632 209.2581 236.2014 272.1572

(Hnf/Hpf)V 1.370130052 1.296301535 1.283756653 1.324405837 1.289846457 1.346430765 1.318479734 1.353072011 1.340044821

(Hnf/Hpf)Re 1.537441677 1.513339277 1.592212691 1.582594713 1.55742004 1.551848589 1.543975997 1.500626002 1.532098163

(Hnf/Hpf)Pe0.5% 13nm 1.599731 1.489318 1.447077 1.5095 1.465359 1.554578 1.51327 1.589468 1.552256

RI PT

Nu_exp-0.5sNu_DB 79.47883 64.97121 142.8185 119.4484 168.6683 136.156 193.8406 155.8581 203.7651 166.9166 227.138 184.7466 254.3888 208.6477 276.3672 231.0418 319.2169 262.5832

SC

h_exp-0.5s K 1389.448 0.134611 2445.348 0.13184 2818.264 0.128659 3284.955 0.130489 3438.53 0.129937 3912.965 0.13265 4349.012 0.131639 4865.766 0.135567 5521.925 0.133197

M AN U

Re^0.8 Pr^0.4 Pe 14144.63 78838.83 27114.33 174758.2 32807.68 216325.8 36219.19 248522.8 39187.97 273075.1 41381.97 298100.7 47507.67 351834.9 49632.14 380732.8 58319.86 459362

TE D

Pr 14.65539 15.71246 17.3558 16.33912 16.62016 15.36753 15.79295 14.33289 15.15173

EP

Vel 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418

AC C

RE 5379.509 11122.27 12464.18 15210.3 16430.35 19398.08 22277.97 26563.57 30317.47

1.058302489 1.099738065 1.108348345 1.135471921 1.101384653 1.176735755 1.143075549 1.138414644 1.156510411

0.5% 13nm0.5% 13nm 1.187536 1.235649 1.283865 1.263487 1.374658 1.249353 1.356829 1.294162 1.329863 1.251252 1.356264 1.358649 1.338573 1.311951 1.26256 1.337308 1.32226 1.339657

ACCEPTED MANUSCRIPT

AC C

EP

TE D

M AN U

SC

RI PT

RE Vel Pr Re^0.8 Pr^0.4 Pe h_exp-0.5l K Nu_exp-0.5lNu_DB Nu_Gen (Hnf/Hpf)V (Hnf/Hpf)Re (Hnf/Hpf)Pe0.5% 50nm 4922.87805 0.699653673 14.59087644 13117.66821 71829.10536 1284.608568 0.128112 77.2099 60.41373 47.33686322 1.422590845 1.525969862 1.593409 9750.402834 1.369898174 14.33141543 22259.076 139737.0737 2046.873625 0.128373 122.7747 103.6243 93.08967541 1.324207643 1.407418926 1.490866 13180.32319 2.081466016 16.62645037 32865.51092 219141.9895 2971.416699 0.124479 183.8058 139.955 131.5091157 1.375573466 1.605362507 1.51001 18148.94292 2.845290758 16.48304217 42084.13815 299149.7916 3849.468936 0.124687 237.7217 180.1457 176.4150658 1.387762624 1.610164159 1.525059 20828.32383 3.363085294 17.08011992 48687.1522 355750.2688 4210.704877 0.123891 261.7002 204.0082 203.0491413 1.327945304 1.577544977 1.45223 24946.99404 3.911925305 16.48847461 54299.40348 411337.8779 5065.259953 0.124683 312.8139 232.3885 235.9882169 1.415484068 1.64262173 1.555391 29650.52862 4.804751989 17.15686942 64873.00241 508710.2476 5982.985833 0.123804 372.1111 271.0997 280.3462331 1.418393995 1.689827704 1.550024

0.5% 50nm 1.120787317 1.123796049 1.18396894 1.210760282 1.123654624 1.237425533 1.230750039

1.202234411 1.194413758 1.381750515 1.404795588 1.334855963 1.43599078 1.466274899

0.5% 50nm 1.255366 1.265231 1.29968 1.330545 1.228819 1.359733 1.344966

ACCEPTED MANUSCRIPT

450 400

0.05% 13nm

RI PT

+20% 350

0.05% 50nm

300

Nu

250

0.2% 50nm

M AN U

-20%

SC

0.2%, 13nm

200

0.3% 13nm

150

0.3% 50nm

100 50 0

20000

EP

10000

AC C

0

TE D

0.5% 13nm 0.5% 50nm

30000

Re

40000

50000

60000

ACCEPTED MANUSCRIPT

0.80 1.29 1.80 2.23 2.66 3.07 3.42 3.97 4.58 Vel 0.70 1.26 1.56 2.31 2.75 3.18 3.28 4.03 4.73

H 329.594 679.478 1183.04 1636.336 2059.792 2462.359 2849.026 3222.952 3586.306 3940.664 4287.216 4626.894 4960.442 5288.47 5611.485 5929.914 6244.122 888.0548 1536.526 1841.624 2463.771 2424.544 2806.421 3320.008 3641.717 4097.511 #VALUE! 888.0548 1447.366 1894.37 2244.16 2586.982 2904.682 3165.46 3561.468 3994.658 #VALUE! 891.291 1425.054 1690.124 2312.586 2655.211 2981.576 3059.105 3605.963 4104.4

RI PT

Nu 24.17023 50.30751 87.59046 121.1518 152.5038 182.3093 210.9375 238.6224 265.5246 291.7607 317.4189 342.5681 367.2635 391.5502 415.4657 439.0417 462.3052 65.75021 113.762 136.351 182.4138 179.5095 207.7831 245.8083 269.6272 303.3734 #VALUE! 65.75021 107.1607 140.2562 166.1542 191.5361 215.0582 234.3658 263.6856 295.7584 #VALUE! 65.98982 105.5088 125.1342 171.2203 196.5877 220.7513 226.4915 266.9799 303.8835

SC

Pe 23304.19 58260.47 116520.9 174781.4 233041.9 291302.3 349562.8 407823.3 466083.8 524344.2 582604.7 640865.2 699125.6 757386.1 815646.6 873907 932167.5 81415 161558.4 202607.8 291511.2 285721 343040.8 423232.1 475102.7 550560.2 #VALUE! 81415 149926.2 209887.1 259401.3 309846.4 358119.5 398750 462052.1 533340.2 #VALUE! 81786.03 147042.8 181992.3 269325.2 320094.7 370008.8 382074.3 469279.1 551717.6

M AN U

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

TE D

Vel

Re Pr 1536.202 3840.506 7681.011 11521.52 15362.02 19202.53 23043.03 26883.54 30724.04 34564.55 38405.06 42245.56 46086.07 49926.57 53767.08 57607.58 61448.09 5366.843 10649.86 13355.82 19216.29 18834.61 22613.1 27899.28 31318.57 36292.7 #VALUE! 5366.843 9883.071 13835.67 17099.62 20424.94 23607.08 26285.43 30458.28 35157.56 #VALUE! 5391.301 9692.999 11996.86 17753.8 21100.51 24390.82 25186.17 30934.68 36368.99

EP

0.20 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50 7.00 7.50 8.00 0.70 1.39 1.74 2.50 2.45 2.94 3.63 4.08 4.72

AC C

V

#VALUE! 948.068 1494.933 1849.591 2302.415 2485.954 2743.895 2933.17 3570.648 3966.328 #VALUE! 808.6815 1441.913 1677.676 2131.788 2409.405 2731.215 3182.288 3675.899 4093.567 #VALUE! 880.739 1401.932 1848.404 2204.555 2460.67 2780.331 3225.505 3697.252 4162.99 939.1149 1287.928 1706.285 2032.511 2382.44 2922.599 3348.653 3729.974 4048.468 957.4169 1463.412 1937.89 2309.62 2475.124 2925.775 3198.882 3539.858

SC

#VALUE! 70.1935 110.6826 136.9409 170.4673 184.0562 203.1538 217.1674 264.3653 293.6608 #VALUE! 59.87353 106.7571 124.2126 157.8343 178.3886 202.215 235.6117 272.1579 303.0814 #VALUE! 65.20856 103.7969 136.853 163.2219 182.1842 205.8514 238.8114 273.7388 308.2214 69.53063 95.35623 126.3307 150.484 176.3922 216.3847 247.9291 276.1615 299.7424 70.88568 108.3488 143.4784 171.0007 183.2544 216.6199 236.8403 262.0856

M AN U

#VALUE! 88349.5 156110.4 203703.9 267845.4 294795.7 333514.1 362515.3 463541.5 528616.3 #VALUE! 72423.01 149220.6 180318.3 243267.8 283492.8 331588.7 401401.6 480683.5 549897.9 #VALUE! 80577.5 144066.6 203540.6 253691.5 291052.6 339059 408227.1 484176.3 561579.8 87307.82 129574.4 184170.1 229190.1 279532.4 360882.9 427801.6 489538.7 542335.7 89439.86 152006.8 215931.6 268893.6 293191.2 361373.2 404019.7 458550.3

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

#VALUE! 5823.962 10290.73 13428.08 17656.26 19432.81 21985.11 23896.86 30556.46 34846.16 #VALUE! 4774.094 9836.557 11886.51 16036.11 18687.72 21858.18 26460.23 31686.46 36249.04 #VALUE! 5311.635 9496.808 13417.31 16723.24 19186.06 22350.63 26910.16 31916.7 37019.1 5755.295 8541.493 12140.41 15108.11 18426.66 23789.25 28200.5 32270.18 35750.54 5895.838 10020.23 14234.12 17725.35 19327.04 23821.57 26632.81 30227.45

AC C

Vel 0.758229 1.339763 1.748217 2.298689 2.52998 2.862267 3.11116 3.978182 4.536663 Vel 0.62 1.28 1.55 2.09 2.43 2.85 3.44 4.13 4.72 Vel 0.691528 1.236401 1.746815 2.177218 2.497857 2.909855 3.503466 4.155273 4.819561 0.75 1.11 1.58 1.97 2.40 3.10 3.67 4.20 4.65 0.77 1.30 1.85 2.31 2.52 3.10 3.47 3.94

RI PT

ACCEPTED MANUSCRIPT

3952.363 998.3795 1857.162 2161.295 2441.875 2624.52 2861.127 3247.374 3540.343 4056.825 889.0085 1521.774 2126.644 2730.868 3121.689 3522.993 4152.754 922.0801 1565.064 1679.369 2249.668 2227.969 2716.355 3066.233 3597.444 4107.391 1048.957 1534.846 1779.974 2223.705 2342.924 2874.383 3095.506 3686.68 3988.522 914.2035 1454.451 1555.335 2199.68 2436.893 2900.474 2917.17 3607.21 3976.339 1004.491 1568.337 1752.876

SC

292.6269 73.91849 137.5014 160.0189 180.7927 194.3154 211.8334 240.4306 262.1216 300.3611 65.82082 112.6698 157.4535 202.1893 231.1251 260.837 307.4635 68.26939 115.875 124.3379 166.562 164.9554 201.1147 227.0192 266.3492 304.1049 77.66317 113.6377 131.7865 164.6397 173.4665 212.8149 229.1865 272.9561 295.304 67.68622 107.6853 115.1546 162.8609 180.4238 214.7467 215.9827 267.0723 294.402 74.371 116.1173 129.7803

M AN U

526290.7 94248.47 204746.7 247484.1 288276.4 315476.6 351419.7 411689.8 458628.9 543735.4 81524.3 159621.8 242534.4 331535.9 391869.9 455821.2 559854.2 85332.71 165317.9 180545.8 260197.3 257064 329335 383187.4 467893.8 552220.2 100254 161337.7 194165.4 256449.1 273749 353456.2 387765.5 482446.4 532316.2 84422.53 150844.2 164034.4 252990.5 287541.3 357471.2 360045 469482.1 530284.5 94970.23 165750.2 190477.5

TE D

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

EP

34692.86 6212.82 13496.81 16314.04 19003.06 20796.08 23165.44 27138.42 30232.63 35842.8 5374.048 10522.2 15987.76 21854.71 25831.9 30047.54 36905.35 5625.096 10897.69 11901.5 17152.1 16945.55 21709.62 25259.55 30843.37 36402.12 6608.704 10635.31 12799.3 16905.02 18045.42 23299.68 25561.34 31802.66 35090.06 5565.097 9943.588 10813.08 16677.03 18954.6 23564.35 23734.02 30948.06 34956.13 6260.398 10926.18 12556.2

AC C

4.52 0.808854 1.757166 2.123945 2.47403 2.707467 3.015936 3.533183 3.936022 4.666418 0.70 1.37 2.08 2.85 3.36 3.91 4.80

RI PT

ACCEPTED MANUSCRIPT

SC

2257.352 2365.024 2768.268 2927.392 3553.058 3961.52 803.2339 1420.566 1499.242 1965.644 2151.631 2579.476 2883.869 3438.884 3743.633 902.7711 1428.844 1703.752 2108.964 2296.182 2705.142 3015.379 3662.634 3992.714 885.5582 1219.384 1485.108 1828.159 2069.969 2588.067 2903.419 3362.635 3600.096 937.577 1421.87 1731.072 2127.646 2306.481 2735.096 2961.279 3457.199 3769.163 898.955 1552.341 1696.466 2012.643 2106.711

M AN U

167.1308 175.1027 204.9583 216.7396 263.0629 293.3049 59.4702 105.1765 111.0015 145.5332 159.3034 190.9804 213.5173 254.6097 277.1729 66.83978 105.7894 126.1432 156.1444 170.0058 200.2846 223.254 271.1758 295.6144 65.56537 90.28131 109.9551 135.3541 153.2573 191.6165 214.9647 248.9643 266.5456 69.41676 105.2731 128.1659 157.5277 170.7683 202.5023 219.2485 255.9657 279.063 66.55724 114.9329 125.6037 149.013 155.9776

TE D

261308.6 276980.4 337221.2 361622.8 460688.7 527815.4 71813.69 146464.2 156673 219804.1 246101.6 308723.1 354914.9 442259 491780.6 83104.93 147531.8 183828.5 240016.5 266939.4 327636.5 375259.8 478516.1 533015.7 81129 121012.5 154829 200757.6 234482 310008.9 357924.9 430035.5 468325 87129.13 146632.3 187520.5 242677.2 268436.8 332177.6 366862.9 445205.2 495976.2 82666.04 163639.6 182846.3 226393.1 239696.1

EP

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

AC C

17225.35 18258.43 22229.48 23838.02 30368.41 34793.37 4733.928 9654.858 10327.82 14489.39 16222.91 20350.89 23395.84 29153.53 32417.97 5478.242 9725.234 12117.9 15821.79 17596.53 21597.66 24736.97 31543.58 35136.17 5347.989 7977.094 10206.26 13233.86 15456.95 20435.66 23594.26 28347.76 30871.78 5743.516 9665.941 12361.27 15997.18 17695.24 21897.01 24183.45 29347.74 32694.54 5449.311 10787.06 12053.15 14923.74 15800.66

RI PT

ACCEPTED MANUSCRIPT

15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17 15.17

286166.1 327696.2 388219.8 452039.2 74314.91 142951.1 197652.6 268687.9 310975.8 374645.1 448248.3

179.7332 200.3137 229.4012 259.1042 61.12155 103.1534 133.6767 170.8961 192.0945 222.9614 257.3645

2427.565 2705.536 3098.406 3499.589 825.5378 1393.241 1805.503 2308.206 2594.523 3011.427 3476.091

AC C

EP

TE D

M AN U

SC

18863.95 21601.59 25591.28 29798.23 4898.807 9423.274 13029.18 17711.79 20499.4 24696.45 29548.34

RI PT

ACCEPTED MANUSCRIPT

ACCEPTED MANUSCRIPT

prdrop_hadla nd

Re

0.017416495 0.050248043 0.101711693 0.17092171 0.262813962 0.313521108 0.341532226 0.406619735 0.488341043

Pr 5000 10000 15000 20000 25000 30000 35000

15.9 15.9 15.9 15.9 15.9 15.9 15.9

Nu_Dittus Boelter RePR Nu_Sonawane 14473.49 63.3086 67.60822657 25199.8 110.2267 117.7127594 34855.4 152.4613 162.8158001 43875.4 191.9158 204.9498181 52450.44 229.4239 245.0053386 60686.78 265.4506 283.4787731 68651.74 300.2902 320.6845051

Blasius Sonawane Present correlation 0.037579 0.037864224 0.039153156 0.0316 0.033191996 0.033615547 0.028554 0.030730953 0.030746813 0.026572 0.029096293 0.028861147 0.025131 0.027888475 0.027478523 0.024011 0.026938929 0.026398151 0.023103 0.026161367 0.025517916

12% 0.043851535 0.037649412 0.03443643 0.032324484 0.030775945 0.029565929 0.028580066

-12% Present Correlation 0.034454778 72.36742707 0.029581681 125.9990088 0.027057195 174.2770243 0.025397809 219.3770162 0.0241811 262.2521973 0.023230373 303.4339233 0.022455766 343.2587085

AC C

EP

TE D

M AN U

SC

RI PT

RE Vel Pr Pe h_exp-p K Nu_exp-p Nu_DB Nu_Gen H-dB H-Gen 6211.352 0.744717 14.82563 92087.21 892.8626 0.105695 65.04601731 73.228819 60.5341941 1005.185 830.9304 10645.42 1.313048 15.26927 162547.7 1545.162 0.105445 112.8333743 114.02112 103.854921 1561.428 1422.21 13365.62 1.895994 17.7493 237230.4 2026.164 0.104281 149.6091968 145.27525 136.771494 1967.47 1852.303 18402.15 2.50717 16.99492 312743.1 2547.879 0.104608 187.5438912 184.39553 180.878658 2505.107 2457.328 21920.01 3.141488 17.94262 393302.4 2975.893 0.1042 219.9080838 216.74782 216.986307 2933.127 2936.354 26077.57 3.465772 16.54483 431449 3241.55 0.104813 238.1383667 241.10514 246.006532 3281.934 3348.651 26721.71 3.62229 16.90049 451610.1 3360.979 0.10465 247.2960579 247.95851 253.655111 3369.983 3447.405 32479.62 3.995471 15.22202 494405.4 3842.865 0.105469 280.5575419 277.97486 290.119402 3807.489 3973.836 34165.06 4.390627 15.95794 545204 4255.455 0.105093 311.7894632 294.97439 309.411637 4025.954 4223.001 36980 4.8 15.9 587982 0.105 331.718015 4523.427 42245.56 5.5 15.9 671704.4 0.105

20% 86.84091248 151.1988106 209.1324291 263.2524194 314.7026367 364.120708 411.9104502

-20% 57.89394166 100.799207 139.4216194 175.5016129 209.8017578 242.7471387 274.6069668

0 550000 550000 550000 550000 550000 550000 550000

0 40000 40000 40000 40000 40000 40000 40000

0 5 5 5 5 5 5 5

1 1 1 1 1 1 1 1

ACCEPTED MANUSCRIPT

RI PT

0.0373168 0.0338451 0.0318496 0.0282757 0.0290005 0.0276256 0.0266313 0.0242645 0.0236647

AC C

EP

TE D

M AN U

SC

RE Nu_exp-0.05s 5547.646 65.07888109 10667.36 110.7126768 12270.8 126.870515 17818.39 167.9756577 17469.05 167.5351509 21709.62 199.861825 25259.55 236.2631742 31067.9 257.8731867 36140.99 286.6818333

f_measur ed

ACCEPTED MANUSCRIPT

RI PT

0.036741 0.034585 0.030481 0.029408 0.027605 0.02645 0.026002 0.025158 0.0241

EP

TE D

M AN U

SC

75.93648 112.1558 140.3751 168.7731 185.5256 224.8539 246.1604 276.9776 316.0861

AC C

RE 6340.269 10563.44 13191.82 17152.91 18753.23 23641.72 25750.78 32135.73 35090.06

f_measu Nu_exp-0.5l red

ACCEPTED MANUSCRIPT

RI PT

0.04218 0.034254 0.031944 0.028686 0.028225 0.02576 0.026575 0.024662 0.023752

EP

TE D

M AN U

SC

63.78673 101.5692 119.4241 168.9436 187.4891 219.6312 223.0068 268.9232 304.0191

AC C

RE 5528.036 10010.13 10975.09 16677.03 19239.19 23732.43 24252.75 31054.79 34706.18

f_measu Nu_exp-0.1s red

ACCEPTED MANUSCRIPT

RI PT

0.036146 0.033284 0.030597 0.028512 0.028001 0.027585 0.026836 0.025112 0.024737

EP

TE D

M AN U

SC

76.10325 116.2627 136.5566 171.6956 187.2706 217.0887 229.5167 284.2824 312.0883

AC C

RE 5970.25 10637.36 12836.75 17473.84 18665.19 22229.48 23838.02 30584 34793.37

f_measu Nu_exp-0.1l red

ACCEPTED MANUSCRIPT

RI PT

0.040188 0.036288 0.035656 0.032057 0.030599 0.029396 0.028127 0.026912 0.026489

EP

TE D

M AN U

SC

61.4864 101.3997 117.0625 144.1866 165.7678 190.284 221.3851 263.1293 285.8465

AC C

RE 4733.928 9593.626 10626.95 14996.81 16811.26 20627.44 24148.21 29555.64 33106.89

f_measu Nu_exp-0.2s red

ACCEPTED MANUSCRIPT

RI PT

0.043287 0.035546 0.03392 0.03166 0.031104 0.029337 0.027827 0.026376 0.025733

EP

TE D

M AN U

SC

66.72749 111.4692 138.1021 167.2666 186.1079 216.0257 243.429 292.318 316.9715

AC C

RE 5444.095 9663.65 12382.43 16153.7 17976.33 21893.18 25091.86 31963.17 35870.93

f_measu Nu_exp-0.2l red

ACCEPTED MANUSCRIPT

RI PT

0.04132 0.039604 0.036113 0.034645 0.032695 0.030365 0.029257 0.027892 0.027248

EP

TE D

M AN U

SC

67.6355 102.797 126.7817 156.1554 174.9715 222.3501 248.0932 286.7741 311.3505

AC C

RE 5364.338 8191.285 10596.97 13717.9 16050.11 21061.97 24187.83 29009.45 31415.48

f_measu Nu_exp-0.3s red

ACCEPTED MANUSCRIPT

RI PT

0.043749 0.037865 0.035277 0.032914 0.032163 0.029747 0.028515 0.027795 0.027292

EP

TE D

M AN U

SC

75.6161 126.2003 156.8825 188.1594 188.3668 239.7737 255.5954 300.8655 330.7055

AC C

RE 5787.31 9788.096 12714.84 16328.61 17695.24 22341.78 24515.61 29897.92 33294.42

f_measu Nu_exp-0.3l red

ACCEPTED MANUSCRIPT

EP

TE D

M AN U

SC

RI PT

Nu_exp-0.5sf_measured 79.47883 0.046918031 142.8185 0.037280862 168.6683 0.036857518 193.8406 0.033851207 203.7651 0.034197865 227.138 0.031778508 254.3888 0.030736776 276.3672 0.029885658 319.2169 0.028428072

AC C

RE 5379.509 11122.27 12464.18 15210.3 16430.35 19398.08 22277.97 26563.57 30317.47

ACCEPTED MANUSCRIPT

RI PT

0.04703 0.038166 0.035425 0.031597 0.031437 0.029085 0.028366

AC C

EP

TE D

M AN U

SC

RE Nu_exp-0.5l 4922.878 77.20989627 9750.403 122.7747195 13180.32 183.8057726 18148.94 237.7216507 20828.32 261.7002016 24946.99 312.8139128 29650.53 372.1110812

f_measu red

ACCEPTED MANUSCRIPT

Highlights 1. Experimental evaluation of heat transfer augmentation of kerosene-Al2O3 nanofluid. 2. Effect of particle size, volume fraction on convective heat transfer properties. 3. Correlations for convective heat transfer coefficient and friction factor.

AC C

EP

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M AN U

SC

RI PT

4. Merit number based assessment to finalize nanofluid particle concentration.