Numerical investigations of heat transfer enhancement in a house shaped- corrugated channel: Combination of nanofluid and geometrical parameters

Accepted Manuscript Numerical investigations of heat transfer enhancement in a house shaped- corrugated channel: Combination of nanofluid and geometrical parameters Raheem K. Ajeel, W.S-I.W. Salim, Khalid Hasnan PII: DOI: Article Number: Reference:

S2451-9049(19)30082-4 https://doi.org/10.1016/j.tsep.2019.100376 100376 TSEP 100376

To appear in:

Thermal Science and Engineering Progress

Received Date: Revised Date: Accepted Date:

15 February 2019 28 June 2019 29 June 2019

Please cite this article as: R.K. Ajeel, W.S-I.W. Salim, K. Hasnan, Numerical investigations of heat transfer enhancement in a house shaped- corrugated channel: Combination of nanofluid and geometrical parameters, Thermal Science and Engineering Progress (2019), doi: https://doi.org/10.1016/j.tsep.2019.100376

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.

1

Article reference: TSEP_2019_73 Article title: Numerical investigations of heat transfer enhancement in a house shapedcorrugated channel: Combination of nanofluid and geometrical parameters.

Raheem K. Ajeel1, 2,*, W. S-I. W. Salim1, Khalid Hasnan1 1

Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Parit Raja, Batu Pahat, Johor, Malaysia. 2

Department of Mechanical Engineering, College of Engineering, University of Babylon, Hilla, Iraq *E-mail

addresses: [email protected] (Raheem K. Ajeel) Phone: +60183599483.

2

Numerical investigations of heat transfer enhancement in a house shaped- corrugated channel: Combination of nanofluid and geometrical parameters

Abstract: Improving the heat transfer rate is one of the main issues at the design stage of different thermal devices for various industries. In this research, a numerical simulation is performed to investigate the combined influences of nanofluid and various parameters designs of a house-shaped corrugated channel on the thermal and hydraulic performance under uniform heat flux of 10 kW/m2 and Reynolds number range of 10000-30000. In respect to the fluid medium, SiO2 nanoparticles are used and investigated with volume fraction up to 0.08. The impacts of geometrical parameters including height-to-width ratio (h/W), pitch-to-length ratio (p/L), and house ratio (e/r) on thermal and hydraulic characteristics are evaluated. The findings show that the (h/W) ratio has more influence on heat transfer promotion than the (p/L) ratio. At Reynolds number 30000, there is a 16.63% increment in average Nusselt number due to a decrease of the (p/L) ratio from 0.175 to 0.075, while the increment 92.28% is achieved by an increase of the (h/W) ratio from 0.0 to 0.05. Heat transfer increases with roof height (r) and decreases with the vertical height of the house-shaped corrugation (e). The findings detect that a h/W of 0.05 with a p/L of 0.075 and e/r=0.6667 are optimum parameters that showed significant improvement in thermal performance. Moreover, new correlations for the Nusselt number and friction factor were developed and reported. Using nanofluid with the current channel is a useful source of reference to enhance thermal performance and produce more compact heat exchangers.

3

Keywords: Geometrical parameters; Enhancement; Nanoparticle; Corrugated; House ratio.

1. Introduction

Today, due to an urgent need to save and manage energy as well as achieve high thermal performance, all efforts of researchers are congruent to achieve the basic goals of increasing efficiency and reducing weight and size. In this light, corrugated surfaces have emerged as one of the best passive ways to increase efficiency and improve heat transfer despite increased pressure. These surfaces are widely used in such fields as heat exchangers, automobile, aerospace, and chemical reactors. The principle of corrugated wall depended on manipulating the fluid direction of the main flow, which helps to induce the secondary flow vortexes, and these vortexes are considered the prime source for enhancing heat transfer. On the other hand, the problem associated with existing techniques on heat transfer performances is heat transfer capabilities of traditional fluids such as water, oil and fluorocarbonbased fluids have been limited due to relatively poor thermal properties. For this purpose, the introduction of nanoparticles into conventional liquids offers a viable solution to improve thermal properties of these liquids. Experimental and numerical studies have shown that the ability and potential of the resulting mixture, called nanofluid, is greater for promoting heat transfer. Numerically and experimentally , many researches have concentrated their efforts on the use of tradational fluids in corrugated channels [1-10]. They reported that the thermal performance enhanced as the corrugated channels replaced with the smooth channel.

4

In the recent years, the nanofluids are used to improve the thermal efficiency. Many studies have numerically and experimentally showed that nanofluids with high volume fraction have higher heat transfer rate in comparison with low volume fraction. For instance, Nakhchi and Esfahani [11],Wang et al. [12], Hu et al. [13], andTavman et al. [14]. Nevertheless, there is no single agreement on the effects of nanoparticle volume concentration to the heat transfer performance of nanofluids. The decreasing trend in convective heat transfer of nanofluids with increase of nanoparticle volume concentration has been widely expressed in most experimental and numerical researches. Pakravan and Yaghoubi [15] noticed the decreasing behavior of Nusselt number with increment of nanoparticles volume fraction while Haddad et al. [16] showed that increasing volume concentration has an adverse effect on heat transfer. Experimentally, using corrugated plate heat exchanger, Pandey and Nema [17] examined the influence of alumina nanofluid on heat transfer at volume fractions of 2, 3, and 4%. They claimed that increasing volume fraction of nanofluid has an adverse influence on heat transfer. On the other hand, some researchers have studied optimization of corrugated channels structure cooled with nanofluid. Numerically, by choosing a sinusoidal wavy channel, Esmaeili et al. [18] clarified through their outcomes that the nanofluid increases heat transfer enhancement. Numerically, Vanaki et al. [19] studied the performance of SiO2- ethylene glycol nanofluid, nanoparticle volume fraction (1-4%), through transversely wavy wall channels. They reported that the wavy channel performance was greatly influenced by changing the phase shift and the wavy amplitude as well as increasing volume fraction. Numerically, by using a microchannel heat sink, Alfaryjat et al. [20] tested the impact of various nanofluids on the PEC. The study was covered volume fraction from 1 to 4%. The results showed that increase volume fraction and decrease nanoparticle diameter leads to thermal resistance improvements.

5

Akdag et al. [21] performed a numerical study to investigate the heat transfer characteristics of CuO-water nanofluid in a trapezoidal-corrugated channel under constant volume fraction and different Reynolds number. The results showed that the secondary flow structures occur in the corrugated walls, and improve the mixture between hot and cold fluids. Ajeel et al. [22] experimentally and numerically analyzed the performance of Al2O3-water nanofluid, nanoparticle volume fraction (1-2%), through different geometries of corrugated channels. The results showed that heat transfer and pressure drop increase with increasing solid particle usage. Numerically, Akdag et al. [23] reported that the heat transfer enhancement of CuO-water nanofluid flow in triangular-wavy channel increases with increasing Reynolds number, and there is a slight increase in pressure drop. Bondareva et al. [24] presented a numerical investigation on Al2O3–water nanofluid, nanoparticles volume fraction (1-5%), in a partially open rectangular cavity with a left heat conducting solid wall of finite thickness and conductivity. It was found that both heat transfer and fluid flow rate decrease as nanoparticles volume fraction increases due to more essential effect of fluid friction in comparison with thermal conductivity growth. Experimentally, using a shell and tube heat exchanger and silver-water nanofluid, Godson et al [25] reported that the increase of volume fraction and Re of silver/water nanofluid leads to increase heat transfer coefficient and effectiveness. Using solar dish collector, another experimental work was done by Pavlovic et al. [26] to test sixteen types of nanofluids, nanoparticle volume fraction 5%, through flat and corrugated absorber tube. The outcomes showed that the maximum exergetic efficiency at 12.29% was recorded for Cu-oil nanofluid at 5% volume fraction. Numerically, by using trapezoidal-corrugated channel, Ahmed et al. [27] remarked that the heat transfer enhancement increases with increase in the volume fraction of the nanoparticle and Reynolds number, while

6

there is slight increase in pressure drop. The study covered nanoparticle volume fraction from 1.0 to 5%. Numerically, using SiO2 - water nanofluid, Ajeel et al. [28] investigated the impact of geometrical parameters on PEC in semicircle-corrugated channel. The results showed that the ratio of height-to-width has a greater effect than the pitch-to-length ratio in terms of PEC. Numerically, by employing a ribbed channel and alumina nanofluid, Manca et al. [29] reported that heat transfer enhancement increases with the particle volume concentration, volume fraction of nanoparticles from 1 to 4%, but it is accompanied by increasing required pumping power. Close to the study of Manca and his team, Ahmed et al. [30] combined a triangular-corrugated channel and different types of nanofluid, to prove that heat transfer was promoted by volume fraction, nanoparticle volume fraction (1-4%), and Reynolds number. Recently, numerically, Ajeel et al. [31-36] have done a series of investigations to examine the effect of nanofluids flow through various forms of corrugated channels namely, semicircle and trapezoidal shapes. The results showed that the corrugated shapes have a clear effect in improving thermal performance and the effect varied according to the shape of the corrugation. On the basis of the above discussion, it can be deduced that almost previous studies focused on test familiar forms of 2-D corrugated channels such as sinusoidal, triangular, and trapezoidal channels. Therefore, the forced convective heat transfer in a house shapedcorrugated channel, when a nanofluid is a working liquid, has not been previously investigated, especially effects of different geometrical parameters. Also, most studies covered volume fraction of nanoparticles in the range of 1 to 5% and did not examine volume fraction more than 0.05. This lack of knowledge motivated this study. Thus, the current study belongs to that small category of studies which have sought to discuss and analyze combined influences of

7

geometrical design parameters and nanofluid on thermal performance under 3-D turbulent forced convective flow. The influence of different design parameters with flowing of silica nanofluid over Reynolds number in the range of 10,000≤ Re ≤30,000 was analyzed and discussed.

2. Geometrical model, assumptions and boundary condition Fig. 1 presented the computational domain of the physical model employed in this study (a), and the test section of the symmetry house shaped- corrugated channel (b). The geometry of corrugated channels consists of parallel walls (upper and lower) and side walls that are flat and unheated. To corrugated section, the upstream and downstream have been added to achieve a fully developed flow condition and prevent flow return in opposite path. Furthermore, in the corrugated section, only upper and lower walls have been heated while the rest of the sections remained unheated. The width of the channel (W) is five times the height (H) which is 10 mm. Concerning the length of channel sections, the corrugated and upstream sections is double length and four times the downstream part, respectively. The overall height of the corrugation and the longitudinal pitch are (h) and (p), respectively. The corrugations pitch is equal to 1.5 times the channel height. The “house” geometry is defined by the wall height (e) and the roof height (r). Table 1 presents the geometrical and design parameters of the current study. Furthermore, the study has adopted the following assumptions: i.

3-D turbulent flow, steady-state and incompressible.

ii.

Single phase model for nanofluid, thermal equilibrium with water and homogenous.

8

Fig. 1. Schematic diagram: (a) geometrical model, (b) Test section (three-dimensional).

Table 1: Design parameters employed in the current study Parameter Channel height Test section length Pitch-to-length ratio Height-to-width ratio House ratio (wall-to-roof)

Terminology H L p/L h/W e/r

Value 10 mm 4W 0.075,0.125,and 0.175 0.0,0.03,0.04, and 0.05 0.25,0.6667,1.5, and 4

As the boundary condition for the models tested here, all the walls except the corrugated walls are regarded as adiabatic as shown in Fig. 1 (a). A constant heat flux condition, 10000 (w/m2), is applied to the corrugated walls including upper and lower walls of test section. Velocity inlet is based on Re which varies from 10000 to 30000. In this respect, uniform velocity is adopted at

9

the inlet of the tested channel as the temperature kept constant at 300 K. Furthermore, turbulence level (turbulent intensity) at the inlet is specified as 0.05 and the non-slip condition is applied to all walls.

3. Governing equations Based on the above boundary conditions, the 3-D governing equations are established to describe the flow problem and heat transfer as follows:

Continuity equation [37]:

𝜕𝑈𝑖 𝜕𝑋𝑖

=0

(1)

Momentum equation [37]:

𝜕(𝑈𝑖 𝑈𝑗 ) 𝜕𝑋𝑗

𝜕𝑝

𝜕

𝜕𝑈

= − 𝜕𝑋 + 𝜕𝑋 (𝜇 𝜕𝑋 𝑖 − 𝜌𝑢𝑖 𝑢𝑗 ) 𝑖

𝑗

𝑗

(2)

Energy equation [37]:

𝜕(𝑈𝑖 𝑈𝑗 ) 𝜕𝑋𝑗

=−

𝜕

(

𝜇 𝜕𝑇𝑖

𝜕𝑋𝑖 𝑃𝑟 𝜕𝑋𝑗

− 𝜌𝑢𝑖 𝑡𝑗 )

(3)

The Reynolds stresses in momentum equation and heat fluxes in energy equation are, respectively, shown below [37]:

10 𝜕𝑈𝑗

𝜕𝑈

𝜌𝑢𝑖 𝑢𝑗 = −𝜇𝑡 ( 𝑋 𝑖 +

𝑋𝑖

𝑗

2

) + 3 𝛿𝑖𝑗 𝑘]

(4)

𝜇 𝜕𝑇

𝜌𝑢𝑖 𝑡𝑗 = − 𝜎 𝑡 𝜕𝑋𝑖 𝜃

(5)

𝑗

The corresponding transport equations in the standard k-ɛ model which are turbulence kinetic energy and energy dissipation [38], are given as: 𝜕𝜌𝑘𝑈𝑖 𝜕𝑋𝑗

𝜕𝜌𝜀𝑈𝑖 𝜕𝑋𝑗

𝜕

𝜇

𝜕𝑘

= − 𝜕𝑋 [(𝜇 + 𝜎 𝑡 ) 𝜕𝑋 ] + 𝜌(𝐺𝑏 − 𝜀) 𝑘

𝑗

𝜕

𝜇

𝜕𝜀

(6)

𝑗

𝜀

= − 𝜕𝑋 [(𝜇 + 𝜎 𝑡 ) 𝜕𝑋 ] + 𝜌 𝑘 (𝑐1𝜀 𝐺𝑏 − 𝑐2𝜀 𝜀) 𝑗

𝑘

(7)

𝑗

𝜕𝑢

𝜕𝑢

𝜕𝑢

𝐺𝑏 = 𝜇𝑡 (𝜕𝑋𝑖 + 𝜕𝑋𝑗 ) 𝜕𝑋𝑖 𝑗

𝑖

𝜇𝑡 = 𝜌𝑐𝜇

𝑗

𝑘2 𝜀

(8)

(9)

where:

𝐶1𝜀 = 1.44, 𝐶2𝜀 = 1.92, 𝐶𝜇 = 0.09 , 𝜎𝑘 = 1.0 , 𝜎𝜀 = 1.3

For the purpose of achieving the aim of the current research to analyze and evaluate the flow characteristics, thermal and hydraulic performance in house shaped-corrugated channel, some of the variables should be displayed: The average Nusselt number, average heat transfer coefficient, and local heat transfer coefficient are determined as below [34, 39]:

11

𝑁𝑢𝑎𝑣 =

ℎ𝑎𝑣 𝐷ℎ

(10)

𝑘ƒ

𝑄𝑎𝑣 = ℎ𝑎𝑣 𝐴𝑐 (∆𝑇)

(11)

𝑞

ℎ(𝑥) = 𝑇 (𝑥)−𝑇 𝑠

(12)

𝑏 (𝑥)

where 𝐴𝑐 ,q, 𝑇𝑠 (𝑥) and 𝑇𝑏 (𝑥) are the surface area of the corrugated wall , the heat flux, local surface wall, and bulk temperatures respectively. In addition, velocity inlet is [27]: 𝑢𝑖𝑛 =

Re 𝜇 𝜌𝐷ℎ

(13)

where Dh represents the hydraulic diameter of the tested channel and can defined as below [22, 28]: Dh =

4Across 𝑃

(14)

Fanning friction factor is [28]: 2𝜏

𝐶𝑓𝑥 = 𝜌u2𝑠

𝑖𝑛

(15)

And friction factor is defined [28]: ƒ = 4𝐶𝑓𝑥

(16)

Also, the pressure drop is [28]: ∆𝑝 = 𝑓

ρ𝐿𝑐𝑜𝑟𝑟 u2𝑖𝑛 2𝐷ℎ

(17)

12

The mathematical formula, which is defined as the ratio of modified structure to the reference structure (straight) by [3], is used to calculate the thermal-hydraulic performance factor (PEC). In this light, (PEC) is defined as follows:

𝑃𝐸𝐶 =

𝑁𝑢 ( 𝑐𝑜𝑟𝑟,𝑎𝑣⁄𝑁𝑢

𝑎𝑣,𝑜

(

)

(18)

∆𝑃𝑐𝑜𝑟𝑟 ⁄∆𝑃 )1/3 0

3. Calculations of nanofluid properties In current study, the thermophysical properties of nanofluids are computed as follows:

i.

Density and heat capacity [28, 36]: 𝜌𝑛𝑓 = (1 − 𝜙) + 𝜙𝜌𝑛𝑝

(19)

(𝜌𝐶𝑃 )𝑛𝑓 = (1 − 𝜙)(𝜌𝐶𝑃 )𝑓 + 𝜙(𝜌𝐶𝑃 )𝑛𝑝 ii.

(20)

Thermal conductivity [36, 40]: keff = kstatic + kBrownian

(21)

(𝑘𝑛𝑝 +2𝑘𝑓 )−2𝜙(𝑘𝑓 −𝑘𝑛𝑝 )

kstatic = kf [ (𝑘

𝑛𝑝 +2𝑘𝑓 )+ 𝜙(𝑘𝑓 −𝑘𝑛𝑝 )

]

𝜅𝑇

𝑘𝐵𝑟𝑜𝑤𝑛𝑖𝑎𝑛 = 5 ∗ 104 𝛽 𝜙𝜌𝑓 𝐶𝑝,𝑓 √𝜌

𝑝 𝑑𝑝

where:

(22)

𝑓(𝑇, 𝜙)

(23)

13

κ = 1.3807*10-23 J/K (Boltzmann constant). Function, 𝑓(𝑇, 𝜙) [36, 40]: 𝑇 𝑇0

𝑓(𝑇, 𝜙) = (2.8217 × 10−2 𝜙 + 3.917 × 10−3 ) ( ) + (−3.0669 × 10−2 𝜙 − 3.391123 × 10−3 ) (24)

iii.

Dynamic viscosity [36, 40]:

𝜇𝑒𝑓𝑓=𝜇𝑓 ∗ (

1∗𝜙−1.03 𝑑𝑝

1−34.87(

𝑑𝑓

)−0.3

)

(25)

Equivalent diameter of based molecule [36, 39]: 6𝑀

𝑑𝑓 =[𝑁𝜋𝜌 ]1/3

(26)

𝑓0

Table 2 and Table 3 present the values of β and the thermophysical properties of different nanoparticles applied in current study immersed in distilled water at 𝜙 =0.08, respectively.

Table 2: Values of β for SiO2 nanoparticles. Nanoparticles type SiO2

𝛽 1.9526(100 𝜙)-1.4594

Concentration (%)

Temperature(K)

1% ≤ 𝜙 ≤ 10%

298K ≤ T ≤ 363K

Table 3: Thermo-physical properties of nanofluid at 𝜙=0.08. Thermo-physical properties Density 𝜌 (kg/m3) Dynamic viscosity, 𝜇(Ns/m2) Thermal conductivity, k(w/m.K) Specific heat, cp (J/kg.K)

SiO2 1094.344 0.004795 0.643072 3622.483

Water 998.2 1.00E-03 0.6 4182

14

4. Numerical analysis and grid independence check

In the current study, 3-D geometry of the tested channel is completed by using SolidWorks premium edition software 2014 × 64 while the heat transfer and flow characteristics of the corrugated models were analyzed by employing commercial CFD code (FLUENT V.16.1). The finite volume method is chosen to deal with the governing equations whereas the second-order upwind scheme is applied for convective terms. In this simulation, the k-ε turbulent model is set with enhanced wall treatment functions to resolve the viscous sublayer and improve near–wall treatment. To couple the velocity and pressure fields, the SIMPLE algorithm is adopted. Moreover, for the diffusion term of the governing equation, second-order upwind scheme is adopted. Using tested channel and at geometrical parameters of p/L=0.075, h/W=0.05, and Re=10000, grid independence test was established with using pure water.

From 162632

elements to 544235 elements, the number of mesh elements has been changed in the test. Accordingly, equation (27) displayed the relative error between (M1) and (M2) which are representing the new outcome and previous outcome of Nusselt number respectively. On the basis of these comparisons in terms of Nuav, , the grid of 413520 elements is set for the simulations as shown in Table 4.

𝑀1 −𝑀2

𝑒=|

𝑀1

| × 100

(27)

15

Table 4: Grid independence test. Grid number 162632 267696 329668 413520 544235

Average Nusselt number 126.1311 126.1546 126.1789 126.1896 126.1971

Relative error% 0.018628 0.019258 0.008479 0.005943

5. Results and discussions In this section, the combined effects of using SiO2-water nanofluid and symmetrical house shaped-corrugated channel with various geometrical parameters is numerically investigated over Re ranges of 10,000–30,000 and 𝜙 of 0–8%. Four values are used for the height-to-width ratio (h/W=0, 0.03, 0.04 and 0.05), three values for the pitch-to-length ratio (p/L=0.075, 0.125 and 0.175), and four values for the house ratio (wall-to-roof) (e/r=0.25, 0.6667, 1.5, and 4) in this study.

5.1 Result validation

For purpose of checking the accuracy of the numerical procedure, simulation outcomes are validated with experimental data obtained from [7] and [9] as displayed in Fig 2 a and b, respectively. Accordingly, the comparison results showed reasonable agreement. To conduct more validation, the nanofluid model in corrugated channel has been compared with numerical data of Abed et al. [39] as presented in Fig 2c. The outcomes have been in good agreement in terms of Nuav. On the basis of Reynolds number range from 5000 to 20000, the viability of using these data for extrapolation to the higher Reynolds number is acceptable. Thus,

16

the present numerical solution is employed for further investigations with targeted channels and nanofluids.

Fig. 2. Comparison between the current work and the outcomes of experimental studies (a) Elshafei et al. [7], and (b) Naphon [9] and with numerical result of (c) Abed et al. [39].

17

5.2 Flow characteristics

Prior to displaying the outcomes of using different geometrical parameters of tested channel, it is substantial to have a comprehension of the flow behaviors first. Fig.3 and 4 show the velocity and isotherm contours for various geometrical parameters of the tested channel at Re of 10000. The velocity represented the master key in drag reduction and heat transfer augmentation. House-shaped corrugations lead to change the fluid path of the main flow which helps to induce the secondary flow vortexes and these vortexes are considered the prime source for enhancing heat transfer. In general, the velocity near the corrugated walls seems affected by the geometrical design of corrugation and Reynolds number. In general, the secondary flows occur in the corrugation where the flow is in the opposite path for the prime flow and the flow becomes more troubled compared with the smooth section. As the flow increases, the secondary flow expands on the main flow. Furthermore, the strong mixing between the core and the corrugated walls will be increased. Due to the different structures between the parallel walls of the tested channel, the recirculation zones occur in different locations. In upper wall, the reverse flows occur inside the corrugation while it is between corrugations regards to the lower wall. In contrast, the reverse flow intensity increases with decreasing p/L ratios. In these respects, p/L=0.075 is the best in generate secondary flow among the other ratios. The opposite trend occurred when discussed the effects of h/W ratios. The small ratio of h/W gave a bad mixing of fluids due to poor generation of recirculation zones. Thus, the h/W=0.05 is the best in this regards. As per the temperature contours, the high-temperature zones are just upstream and downstream of the house-shaped corrugations for all cases, depending on the recirculation flows. Also, fluid separation occurs between corrugations, after and before, causing recirculation in the

18

channel flow (in the opposite path of prime flow). In this case, the mixing between the core which is cold and the corrugated walls which are hot is excellent. The p/L=0.075 and h/W=0.05 ratios showed a relatively low temperature near wall due to efficient heat transfer improvement in this case. As a result, the temperature gradients increment rises with Re due to the reduction of thermal boundary layers as well as the induction of a secondary flow. This is similar to the pervious study of Naphon [9].

Fig. 3. Streamlines (left) and isotherms (right) contours for SiO2-water nonofluid flow in symmetry house shaped–corrugated channel with different pitch-to-length ratio (p/L).

19

Fig. 4. Streamlines (left) and isotherms (right) contours for SiO2-water nonofluid flow in symmetry house shaped –corrugated channel with different height –to-width ratio (h/W).

Fig.5 and 6 show the turbulent kinetic energy and vorticity contours for various geometrical parameters of the tested channel at Re of 10000. One can conclude from these figures that the intensity of turbulence has been significantly affected by geometrical design parameters of

20

corrugation, as well as caused more production of turbulent heat transfer. With this system, the higher rate of turbulent intensity is shown near the corrugation, before and after respects to lower wall, whereas in case of upper wall, turbulent intensity is observed inside corrugations. Generally, the turbulent intensity depends on the location of the corrugation in the upper and lower walls. In this way, there is a difference between turbulent kinetic energy distribution nearby upper and lower walls. Furthermore, important factors helped to generate more turbulent kinetic energy, which are flow type and Reynolds number. Accordingly, high Re and turbulent flow lead to enhance momentum and heat transfer among fluid layers, core flow and wake flow, which makes the turbulence back in the opposite path of the flow. On that basis, the forms of p/L=0.075 and h/W=0.05 is the best among the other forms of the tested channel in terms of turbulent energy. Moving to the vorticity contours, the vorticity fields are shown to be symmetric about axial direction for all forms, due to symmetrical of the corrugation in the upper and lower wall. Also, the flow profile of the vorticity contours detects an excellent correlation with turbulent kinetic energy. In general, every vorticity generated in flow path is a pure phenomenon linked with geometrical structures of the tested channel and flow circumstances, and influenced by them. Hence, the generated vortices have significant benefit to enhance heat exchange due to the positive impact to improve process of fluid blending inside channel. On the other hand, the shear stress rose because the working fluid is driven toward the walls, which generates more friction. Thus, the primary point is the thermal performance of the tested channel strongly depended on generation of vortices where it increased as the vortices generation increased. Among the tested channels, the forms of p/L=0.125 and h/W=0.03 has the lowest one in terms of vorticity generation whereas the shapes of p/L=0.075 and h/W=0.05 showed the highest rate.

21

(a)

(b)

(c)

Fig. 5. Turbulent kinetic energy (left) and vortices (right) contours for different pitch –to-length ratio (p/L) of tested channel at Re = 10000 (a) p/L=0.075, (b) p/L=0.125, and (c) p/L=0.175.

22

(a)

(b)

(c)

Fig. 6. Turbulent kinetic energy (left) and vortices (right) contours for different height –to-width ratio (h/W) of tested channel at Re = 10000 (a) h/W=0.03, (b) h/W=0.04, and (c) h/W=0.05.

5.3 Geometric parameters influence 5.3.1 Influence of pitch –to-length (p/L) ratio

The corrugation ratio (p/L) varied from 0.075 to 0.175 while the h/W ratio is held constant (h/W=0.05) and the house ratio was held constant (e/r=0.6667.

23

The computed Nuav allocation versus Reynolds number for various parameters of p/L ratio is shown in Fg.7a. Generally, the increase of Re has strongly affected the increase in Nuav. In other words, the average Nu for all forms of tested parameters increases with Re due to an increase of wall temperature gradient. The trouble flow is related with increases in velocity which generate improvement of heat transfer as a result. Due to no corrugations, the flat channel flow offered the lowest rates of Nuav among the tested channels. In contrast, the channels which have corrugations lead to change the fluid direction of the main flow which helps to induce the secondary flow vortexes and these vortexes are considered the prime source for enhancing heat transfer. In contrast, p/L ratio of 0.075 has the highest ratings of Nuav. The low length of flat wall could explain the high ratings of Nuav. Moreover, high velocity is another source for this increase. High velocity means low density where the latter correlated to the increase of Nuav. In addition, the intense influence of the secondary regions creates the problems associated with an increase in the velocity of silica nanofluid. As a result, the temperature gradient on the tested walls enhances, which accordingly improves the Nuav. For instance, at Re=30000, Nuav increased from 522 to 608. Also, when p/L varied from 0.175 to 0.075, by 16.63% increment in Nuav at Re=30000. Furthermore, at particular ratio p/L=0.075 and p/L=0.175, 64.54% and 58.64% Nuav increase when Re varied from 10000 to 30000, respectively. The deviation of pressure drop due to test different ratio of a p/L is shown in Fig. 7b. Clearly, for all ratio of p/L, pressure drop increases as Reynolds number increases. In contrast, the ∆p of p/L=0.175 is superior to p/L=0.125 and p/L=0.075, which is consistent with the previous study [35, 36]. Additionally, the ∆p obtained by p/L=0.075 is the best among the tested ratio, where it recorded the minimum values of ∆p.

24

Fig. 7. The impact of various values of pitch –to-length ratio (p/L) of symmetry house shapedcorrugated channel on (A) Nu, (B) ∆p, (C) Nuer, and (D) PEC. Fig.7(c) shows the enhancement ratio of 𝑁𝑢𝑎𝑣 of silica nanofluid flow in the considered channel at various p/L ratios to that of the base fluid flow in the smooth channel. For all cases, the ER decreases with a rise in Re. In addition, there is a decrease in the ER for all tested cases with increasing Reynolds number. According to the figure, the small ratio of p/L offered the highest

25

ER among the rest ratio. As mentioned earlier, the fluid mixing is stronger in case of a small p/L ratio which has effect to produce stronger turbulence and more friction than the large p/L ratio. Fig.7 (d) presents the variation of the PEC for all p/L ratios tested in current study. Generally, the PEC decreases with Re for all types of p/L ratios. In this respect, a reduction in the PEC of about 8.47%, 8.6%, and 8.13% is obtained for p/L=0.075, p/L=0.125, and p/L=0.175, respectively, at Re ranges 10000 to 30000. Here, it should be noted that the peak values of PEC for all ratio types are at Re=10000. The p/L=0.075 offers the best performance at 2.89 and Re=10000. In this point, it is recommended to use p/L=0.075 as opposed to the other kinds studied here since it the best in terms of PEC.

5.3.2 Influence of height –to-width (h/W) ratio

In order to discuss the influences of various h/W ratios for the considered channel on the flow and thermal fields, several parameters are kept fixed including p/L =0.075, e/r = 0.6667, and 𝜙 = 0.08. The investigation covered four values of h/W ratio of 0.0, 0.03, 0.04, and 0.05. Fig.8 (a) shows the simulation results of average Nusselt number of SiO2-water nanofluid for various h/W ratios. Generally, at particular Re, there is a high increase of Nuav for all cases. In contrast, h/W=0.05 has the highest ratings of Nuav. In addition, at Re=30000, due to increases h/W from 0.0 to 0.05, there is a 92.27% increment in Nuav . As observed in Fig. 8, it’s linked to the increased amount of flow blending. In light of that, the temperature gradients changes across the channel due to enhance the flow mixing nearby the corrugations. Fig.8 (b) presents the ∆p against Reynolds number with various h/W ratios. Generally, the ∆p rises with Re for all ratios. In addition, the ∆p obtained by smooth channel (h/W=0.0) is

26

the best among the tested cases, where it recorded the minimum values of ∆p. In contrast, the ∆p of h/W=0.05 is superior to the rest of tested ratios. When h/W=0.04,0.03, the recirculation zones and fluid mixing is less than for ratio of h/W=0.05.

Fig.8. The impact of various values of height –to-width ratio (h/W) of symmetry house shapedcorrugated channel on (A) Nu, (B) ∆p, (C) Nuer, and (D) PEC.

27

Fig.8 (c) displays the enhancement ratio of 𝑁𝑢𝑎𝑣 of different h/W ratios. For all cases, the ER decreases with increasing Reynolds number. According to the figure, h/W=0.05 offered the highest ER among the others ratio. At Re = 10000 for h/W = 0.05, ER is superior by a factor of 3 compared to smooth channel with base fluid. Fig.8 (d) illustrates the variation of the PEC for all h/W ratios tested in current study. Generally, the PEC decreases with Re for all types of cases. In this respect, a reduction in the PEC of about 1.82%, 7.46%, 7.54%, and 8.47% is obtained for h/W=0, 0.03, 0.04, and 0.05, respectively, at Re ranges 10000 to 30000. Here, it should be noted that the peak values of PEC for all h/W ratios are at Re=10000. The h/W=0.05 offers the best performance at 2.89 and Re=10000. In this point, it is recommended to use it as opposed to the other kinds studied here since it the best in terms of PEC.

5.3.3 Effect of house ratio (e/r) Since the corrugation ratios of p/L=0.075 and h/W= 0.05 for symmetry house shaped-corrugated channels offered better performance, it is employed to investigate the impact of other geometrical parameters which is the house ratio (e/r). This section evaluates the influences of four different house ratios (e/r) of 0.25, 0.6667, 1.5, and 4 on 𝑁𝑢𝑎𝑣 ,𝑁𝑢𝑒𝑟 , ∆p, and PEC . The average Nusselt number against Reynolds number for different house ratios (e/r) for the tested channel are displayed in Fig. 9a. The e/r values varied from 0.25 to 4.0 mm. Nuav increases with Reynolds number for each house ratio corrugation (e/r). As shown in Fig. 9a, the lowest Nu occurs at a house ratio of 1.5 due to poor fluid mixing. At house ratio e/r=4, the Nusselt number is slightly increased due to an increase in the wall temperature gradient. With e/r=0.66667, the Nusselt number increases due to improved fluid mixing near the corrugated walls. The heat transfer enhancement of house ratio e/r = 0.25 is superior to the house ratios e/r =

28

0.66667, 4, and 1.5. Due to the effect of reverse flows that promote fluid blending and enhance the wall temperature gradient when e/r=0.25 as shown in Fig. 10. In addition, it is observed that larger temperature change zones are present in channels with house ratios of e/r=0.25 at the abovementioned areas.

Fig.9. The impact of various values of house ratio (wall –to-roof ratio) (e/r) of symmetry house shaped- corrugated channel on (A) Nu, (B) ∆p, (C) Nuer, and (D) PEC.

Fig. 9b indicates pressure drop against Reynolds number for various house ratio corrugations. Pressure drop for each value of (e/r) increase with increasing Reynolds number. Additionally,

29

the lowest value of ∆p occurs at e/r=0.66667. At e/r=1.5, the pressure drop is slightly increased due to the effect of the recirculation zones. At e/r=0.25, the corrugated channel records the highest pressure drop. The streamlines in Fig. 8 provide an explanation for this increase. At e/r=0.25, due to the effect of heating source, the isotherms become thinner and denser which leads to increase temperature gradients. Accordingly, the outer flow is more disturbed and thus increases the friction loss.

Fig. 10. Streamlines (left) and isotherms (right) contours for SiO2-water nonofluid flow in symmetry house shaped –corrugated channel with (a) e/r=0.25, (b) e/r=0.66667,(c) e/r=1.5, and (d) e/r=4.

30

Fig. 9c presents the average Nusselt number enhancement ratio for the silicon dioxide-water nanofluid in a symmetrical house shaped corrugated channel to the average Nusselt number for base fluid in a smooth channel (h=0) with various house ratio values. In general, the ER for all values of (e/r) decreases with increasing Reynolds number. Furthermore, it is observed that the house ratio of e/r=0.25 has a better enhancement ratio than e/r=0.66667, 4, and 1.5 due to better fluid mixing. Fig. 9d demonstrates variations of PEC against Reynolds number with various house ratio corrugations under consideration. PEC for all tested ratios decreases with increasing Reynolds number. There are 6.97%, 7.5%, 8.47%, and 9.0% reductions in PEC for house ratios 0.25, 1.5, 0.66667, and 4, respectively at Re 10000-30000. In addition, it is seen that the housing ratio of e/r=0.66667 records the best PEC for all ranges of Re and the peak value is 2.89 at Re=10000.

5.4 Influence of various volume fractions of SiO2

On the basis of the above discussed, since the house-shaped corrugated channel with parameters of p/L=0.075, h/W=0.05 and e/r=0.6667shows better performance, it is employed to investigate the influences of various 𝜙 of SiO2 nanoparticles. The simulation results of average Nusselt number with Reynolds number for different volume fraction of SiO2 at p/L=0.075, h/W=0.05 and e/r=0.6667 is illustrated in Fig. 11(a). As the volume fraction increases, Nusselt number is strongly increased for all Reynolds number. The high thermal conductivity and the Brownian motion are the real supporters of this increase. In this respect, the Brownian motion is defined as the random motion of nanoparticles that are

31

immersed in the base fluid and this means increase in thermal conductivity of nanofluid according to Eq. (21) due to the extra impact of Brownian motion.

Fig.11. The impact of different volume fraction of SiO2 on (a) Nuav , (b) ∆p, (c) Nuer, and (d) PEC.

Fig. 11 (b) displays the results of pressure drop against Reynolds number with different volume fractions of SiO2 nanoparticles. Clearly, the findings showed a marked enhancement in ∆p with the raising of volume fraction and Reynolds number. The viscosity of nanofluid should be takes into account to explain these increases. As predicted, high viscosity is associated with the generation of recirculation flow due to increase volume fraction. Additionally, the intensity of

32

recirculation zones develops and become stronger with increasing the volume fraction of nanoparticles leading to further increment in the pressure drop as well. Previous study [19] has been found similar outcomes. Fig.11 (c) demonstrates the ratio of average Nusselt number for various volume fractions of SiO2-water nanofluid flow in the considered channel to that of the base fluid flow in the smooth channel. The ER represents the performance of heat transfers for the tested cases. For all cases, the ER decreases with increasing Reynolds number. When the volume fraction varied from 0.0% to 4.0%, the ER increases from 1.92 to 2.52 at Re=10000. Fig. 11 (d) presents the PEC against Reynolds number which has been extracted for different volume fraction of silicon dioxide –water nanofluid. Clearly, the PEC of nanofluids at various volume fraction over the Re range is superior to the pure water (𝜙 = 0.0). The outcomes showed that the PEC has a decrease with increasing Reynolds number for all tested fluids. Accordingly, in all cases, the PEC is higher than the unity, which indicates the effectiveness of the various volume fraction of nanofluids in improving system performance. In other words, as the volume fraction increases, the PEC shows an increase due to the increase in heat transfer is more than the increase in friction loss. Therefore, SiO2-water nanofluid with 𝜙 = 0.08 provids the best PEC AT Re=10000 of 2.89.

5.5 Correlations of Nusselt number and friction factor

Numerically, the simulation outcomes of Nusselt number and friction factor are employed to develop new correlations by using least square method of regression analysis as shown below:

33 𝑝 −0.153

𝑁𝑢 = 0.115𝑅𝑒 0.935 𝑃𝑟 −0.125 (1 − 𝜑)−8.637 (𝐿 )

ℎ 0.598 𝑒 −0.03

(𝑊)

𝑝 −0.034

𝑓 = 2784.008𝑅𝑒 −0.197 𝑃𝑟 −7.321 (1 − 𝜑)−187.106 (𝐿 )

(𝑟 )

ℎ 0.377 𝑒 −0.009

(𝑊)

(𝑟 )

(26)

(27)

Maximum deviation for Nusselt number and friction factor are ±5.1% and ±11.2%, respectively which indicated a good agreement with the numerical data. The correlations are valid for SiO2water nanofluid with ranged 0 ≤ 𝜙 ≤ 0.08 under turbulent flow regime with 10,000 ≤ Re ≤ 30,000 through a symmetrical house shaped–corrugated channel.

6. Conclusion Numerically, 3-D turbulent forced convective flow of silica nanofluid in the house shaped corrugated channels was evaluated by a CFD approach. The main objective of the current study is to investigate the combined influences of nanofluid and geometrical parameters of the channel considered here. Several geometrical parameters, namely, pitch-to-length ratio, height-to-width ratio, and house ratio (wall-to-roof) have been tested by using SiO2-water nanofluids. The Reynolds number range was 10,000–30,000 and 𝜙 was 0–8%. The major conclusions are derived as: 

The findings showed that increases Reynolds number and corrugated height–towidth ratios have a marked influence to improve average Nusselt number, along with pressure drop.



The p/L ratio had displayed opposite trend compared to h/W ratio, as p/L increases, heat transfer decreases.



The h/W ratio had a greater impact than the p/L ratio in terms of PEC.

34



There were 1.83%, 7.46%, 7.54%, and 8.47% reductions in PEC for h/W=0.0, 0.03, 0.04, and 0.05, respectively at Reynolds numbers 10000-30000.



The thermal performance factor (PEC) increased with increases in house roof (r) and decreases in vertical height (e) of the house wall with a ratio of 1.5 to 1.



The SiO2-water nanofluids show a better thermal performance compared to the base fluid. It is interesting to explain that the thermal performance of the targeted channel is more noticeable at higher volume fractions compared to lower ones.



Of all the investigated design parameters, the ratios of h/W = 0.05, p/L = 0.075, and house ratio e/r=0.6667 were optimum parameters with a great effect on PEC.



New correlations for Nusselt number and friction factor were developed using nanofluids flow inside the house shape-corrugated channel.

Finally, it can be considered that the current results may help nicely for designing and fabricating more compact heat exchangers via best selection of enhanced channels. Acknowledgement: The authors would like to sincerely thank Universiti Tun Hussein Onn Malaysia and the Ministry of Higher Education for sponsoring this study under the Grants (FRGS 1589).

Nomenclature

35

A

area, mm2

𝑐1𝜀 , 𝑐2𝜀 , 𝐶𝜇 , 𝜎𝐾 , 𝜎𝜀

Model constants

Cp

specific heat capacity (J/kg.k)

CFD

computational fluid dynamic

Cf

skin friction coefficient

dp

Particles diameter, nm

df

equivalent diameter of a base fluid molecule,𝜇𝑚

h

Total height of corrugation, mm

HTC

heat transfer coefficient, (W/m2.K)

H

height of channel, mm

k

turbulent kinetic energy , (m2/s2)

Nu

Nusselt number

p

Pitch of corrugation, mm

∆p

Pressure drop(pa)

Pr

Prandtl number, pr =

p/L

Pitch-to-length ratio

q

heat flux, (W/m2)

h/W

Height-to-width ratio

Re

Reynolds number, Re =

SiO2

silicon dioxide

T

temperature, K

u,v,w

velocity component, (m/s)

𝑐𝑝 𝜇 𝑘

𝜌 𝑢𝑖 𝐷ℎ 𝜇

36

W

width of tested channel, mm

Greek symbols 𝜇

Dynamic viscosity of the fluid, (kg/m.s)

𝜌

Density, (kg/m3)

𝜀

Turbulent kinetic dissipation (m2/s2)

𝜏

Wall shear stress (pa)

𝜎𝑘

diffusion prandtl number for k

𝜙

Nanoparticle volume fraction

Subscripts av

average

b

bulk

er

Enhancement ratio

in

inlet

nf

nanofluid

np

nanoparticles

o

Straight channel

out

outlet

s

start point of corrugated wall

x

local value

37

References [1]Piroozfam N, Shafaghi AH, Razavi SE. Numerical investigation of three methods for improving heat transfer in counter-flow heat exchangers. International Journal of Thermal Sciences. 2018 Nov 1; 133:230-9. [2]ALI, M., RAMADHYANI S., 1992. Experiments on Convective Heat Transfer in Corrugated Channels. Experimental Heat Transfer, 5.175–93. [3]Akbarzadeh M, Rashidi S, Esfahani JA. Influences of corrugation profiles on entropy generation, heat transfer, pressure drop, and performance in a wavy channel. Applied Thermal Engineering. 2017 Apr 1; 116:278-91. [4]Bayrak E, Olcay AB, Serincan MF. Numerical investigation of the effects of geometric structure of microchannel heat sink on flow characteristics and heat transfer performance. International Journal of Thermal Sciences. 2018 Oct 6. [5]Islamoglu Y, Parmaksizoglu C. The effect of channel height on the enhanced heat transfer characteristics in a corrugated heat exchanger channel. Appl Therm Eng 2003; 23(8):979–87. [6]Khoshvaght-Aliabadi M, Nozan F. Water cooled corrugated minichannel heat sink for electronic devices: Effect of corrugation shape. International Communications in Heat and Mass Transfer. 2016 Aug 1; 76:188-96. [7]Elshafei EAM, Awad MM, El-Negiry E, Ali AG. Heat transfer and pressure drop in corrugated channels. Energy 2010; 35(1):101–10. [8]Zheng N, Liu P, Shan F, Liu Z, Liu W. Numerical investigations of the thermalhydraulic performance in a rib-grooved heat exchanger tube based on entropy generation analysis. Applied Thermal Engineering. 2016 Apr 25; 99:1071-85.

38

[9]Naphon P. Heat transfer characteristics and pressure drop in channel with V corrugated upper and lower plates. Energy Convers Manag 2007; 48(5):1516–24. [10]Dizaji HS, Jafarmadar S, Mobadersani F. Experimental studies on heat transfer and pressure drop characteristics for new arrangements of corrugated tubes in a double pipe heat exchanger. International Journal of Thermal Sciences. 2015 Oct 1; 96:211-20. [11]Nakhchi ME, Esfahani JA. Cu-water nanofluid flow and heat transfer in a heat exchanger tube equipped with cross-cut twisted tape. Powder Technology. 2018 Nov 1; 339:985-94. [12]Wang X, Xu X, S. Choi SU. Thermal conductivity of nanoparticle-fluid mixture. Journal of thermophysics and heat transfer. 1999 Oct; 13(4):474-80. [13]Hu P, Shan WL, Yu F, Chen ZS. Thermal conductivity of AlN–ethanol nanofluids. International Journal of Thermophysics. 2008 Dec 1; 29(6):1968-73. [14]Tavman I, Turgut A, Chirtoc M, Schuchmann HP, Tavman S. Experimental investigation of viscosity and thermal conductivity of suspensions containing nanosized ceramic particles. Archives of Materials Science. 2008 Dec; 100(100). [15]Pakravan HA, Yaghoubi M. Analysis of nanoparticles migration on natural convective heat transfer of nanofluids. International Journal of Thermal Sciences. 2013 Jun 1; 68:79-93. [16]Haddad Z, Abu-Nada E, Oztop HF, Mataoui A. Natural convection in nanofluids: are the thermophoresis and Brownian motion effects significant in nanofluid heat transfer enhancement?. International Journal of Thermal Sciences. 2012 Jul 1; 57:152-62.

39

[17]Pandey SD, Nema VK. Experimental analysis of heat transfer and friction factor of nanofluid as a coolant in a corrugated plate heat exchanger. Experimental Thermal and Fluid Science. 2012 Apr 1; 38:248-56. [18]Esmaeili M, Sadeghy K, Moghaddami M. Heat Transfer Enhancement of Wavy Channels Using Al 2 O 3 Nanoparticles. Journal of Enhanced Heat Transfer. 2010; 17(2). [19]Vanaki SM, Mohammed HA, Abdollahi A, Wahid MA. Effect of nanoparticle shapes on the heat transfer enhancement in a wavy channel with different phase shifts. Journal of Molecular Liquids. 2014 Aug 1; 196:32-42. [20]Alfaryjat AA, Mohammed HA, Adam NM, Stanciu D, Dobrovicescu A. Numerical investigation of heat transfer enhancement using various nanofluids in hexagonal microchannel heat sink. Thermal Science and Engineering Progress. 2018 Mar 1; 5:252-62. [21]Akdag U, Akcay S, Demiral D. Heat transfer enhancement with nanofluids under laminar pulsating flow in a trapezoidal-corrugated channel. Progress in Computational Fluid Dynamics, an International Journal. 2017; 17(5):302-12. [22]Ajeel RK, Salim WI, Hasnan K. Experimental and numerical investigations of convection heat transfer in corrugated channels using alumina nanofluid under a turbulent flow regime. Chemical Engineering Research and Design. 2019 Jun 13. https://doi.org/10.1016/j.cherd.2019.06.003. [23]Akdag U, Akcay S, Demiral D. HEAT TRANSFER IN A TRIANGULAR WAVY

CHANNEL

WITH

CuO-WATER

NANOFLUIDS

PULSATING FLOW. Thermal Science. 2019 Jan 1; 23(1).

UNDER

40

[24]Bondareva NS, Sheremet MA, Oztop HF, Abu-Hamdeh N. Heatline visualization of natural convection in a thick walled open cavity filled with a nanofluid. International Journal of Heat and Mass Transfer. 2017 Jun 1; 109:175-86. [25]Godson L, Deepak K, Enoch C, Jefferson B, Raja B. Heat transfer characteristics of silver/water nanofluids in a shell and tube heat exchanger. Archives of Civil and Mechanical Engineering. 2014 May 1; 14(3):489-96. [26]Pavlovic S, Bellos E, Loni R. Exergetic investigation of a solar dish collector with smooth and corrugated spiral absorber operating with various nanofluids. Journal of Cleaner Production. 2018 Feb 10; 174:1147-60. [27]Ahmed MA, Shuaib NH, Yusoff MZ, Al-Falahi AH. Numerical investigations of flow and heat transfer enhancement in a corrugated channel using nanofluid. International Communications in Heat and Mass Transfer. 2011 Dec 1; 38(10):1368-75. [28]Ajeel RK, Salim WI, Hasnan K. Design characteristics of symmetrical semicircle-corrugated channel on heat transfer enhancement with nanofluid. International Journal of Mechanical Sciences. 2019 Feb 1; 151:236-50. [29]Manca O, Nardini S, Ricci D. A numerical study of nanofluid forced convection in ribbed channels. Applied Thermal Engineering. 2012 May 1; 37:280-92. [30]Ahmed MA, Yusoff MZ, Ng KC, Shuaib NH. Numerical investigations on the turbulent forced convection of nanofluids flow in a triangular-corrugated channel. Case Studies in Thermal Engineering. 2015 Sep 1; 6:212-25. [31]Ajeel RK, Salim WI, Hasnan K. Impacts of corrugation profiles on the flow and heat transfer characteristics in trapezoidal corrugated channel using nanofluids.

41

Journal of Advanced Research in Fluid Mechanics and Thermal Sciences.2018.49 (2), pp. 170-179. [32]Ajeel RK, Salim WS. A CFD study on turbulent forced convection flow of Al2O3-water nanofluid in semi-circular corrugated channel. InIOP Conference Series: Materials Science and Engineering 2017 Sep (Vol. 243, No. 1, p. 012020). IOP Publishing. [33]Ajeel, R.K., Salim, W.I., Hasnan, K., 2018c. Thermal performances comparison in various types of trapezoidal corrugated channel using nanofluids. Int. Rev. Mech. Eng. 12 (8), 672–683. [34]Ajeel, R.K., Salim, W.S., Hasnan, K., 2018d. Numerical investigations of flow and heat transfer enhancement in a semicircle zigzag corrugated channel using nanofluids. Int. J.Heat Technol. 36 (December (4)), 1292–1303. [35]Ajeel, R.K., Salim, W.I., Hasnan, K., 2019c. Influences of geometrical parameters on the heat transfer characteristics through symmetry trapezoidalcorrugated channel usingSiO2-water nanofluid. Int. Commun. Heat Mass Transf. 101(February), 1–9. [36]Ajeel RK, Salim WI, Hasnan K. Thermal and hydraulic characteristics of turbulent nanofluids flow in trapezoidal-corrugated channel: Symmetry and zigzag shaped. Case Studies in Thermal Engineering. 2018 Sep 1; 12:620-35. [37]Schlichting H, Gersten K, Krause E, Oertel HJ, Mayes C. Boundary Layer Theory Springer. Eigth Revised and Enlarged Edition. 2000.

42

[38]Launder BE, Sharma BI. Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Letters in heat and mass transfer. 1974 Nov 1; 1(2):131-7. [39]Abed AM, Alghoul MA, Sopian K, Mohammed HA, Al-Shamani AN. Design characteristics of corrugated trapezoidal plate heat exchangers using nanofluids. Chemical Engineering and Processing: Process Intensification. 2015 Jan 1; 87:88103. [40]Vajjha RS, Das DK, Kulkarni DP. Development of new correlations for convective heat transfer and friction factor in turbulent regime for nanofluids. International Journal of Heat and Mass Transfer. 2010 Oct 1; 53(21-22):4607-18.