water nanofluid in a ribbed flat-plate solar collector

Accepted Manuscript Flow and heat transfer analysis of TiO2/water nanofluid in a ribbed flat-plate solar collector Farzad Bazdidi-Tehrani, Arash Khabazipur, Seyed Iman Vasefi PII:

S0960-1481(18)30062-4

DOI:

10.1016/j.renene.2018.01.056

Reference:

RENE 9661

To appear in:

Renewable Energy

Received Date: 29 September 2017 Revised Date:

9 December 2017

Accepted Date: 16 January 2018

Please cite this article as: Bazdidi-Tehrani F, Khabazipur A, Vasefi SI, Flow and heat transfer analysis of TiO2/water nanofluid in a ribbed flat-plate solar collector, Renewable Energy (2018), doi: 10.1016/ j.renene.2018.01.056. 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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Flow and Heat Transfer Analysis of TiO2/Water Nanofluid in a

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Ribbed Flat-Plate Solar Collector

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Farzad Bazdidi-Tehrani , Arash Khabazipur, Seyed Iman Vasefi

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School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

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[email protected],

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[email protected]

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[email protected]

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Address correspondence to Professor Farzad Bazdidi-Tehrani, E-mail: [email protected], Phone number: + 98 21 7749 1228, Fax number: + 98 21 7724 0488

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Abstract

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The present paper investigates the turbulent forced convection of TiO2/water nanofluid through a

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ribbed flat-plate solar collector numerically. A three-dimensional simulation of solid flat-plate

5

with flow through the plain and ribbed duct has been performed. The scale-adaptive-simulation

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approach has been employed to simulate the flow turbulence. The velocity and temperature

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profiles, Nusselt number and the efficiency of solar flat-plate solar collector have been studied

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by using plain and ribbed ducts at different Reynolds number and nanoparticles volume fraction.

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Results indicate that wake circulation region in the back of the rib is intensified at higher

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Reynolds number leading to an enhancement in the convective heat transfer. Moreover, the

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efficiency of flat-plate solar collector increases with the nanoparticles volume fraction whilst an

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enhancement in the efficiency of the ribbed duct is approximately 10% higher than that of the

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plain duct. This enhancement varies for different nanofluids such that the CuO/water nanofluid

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provides a higher thermal efficiency than that of TiO2/water.

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Keywords: Nanofluid, Flat-plate solar collector, Ribbed duct, SAS approach, Turbulent flow

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1. Introduction

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In the recent decades, seeking new sources of energy has been among the most attempted goals

3

of scientists and technologists. This is even more highlighted in the case of renewable energy

4

when sustainable development is desired as a future perspective. Solar energy has attracted a

5

great deal of attention, as compared with the other renewable energy resources. As the greatest

6

fusion reactor in the solar system, sun emits a quantity of

7

fraction of less than

8

of radiation received on earth can fulfil one year of energy demand on the planet [2]. Recordings

9

from the prehistoric eras to the present show the attempts of human beings to use this solar

10

energy[1,3–5]. For this purpose, devices have been developed in the form of Solar collector

11

systems, Solar PV cells, Desalination systems, etc. [6–9]. Solar collectors are considered as heat

12

exchangers which convert the solar radiation energy to the transport medium in the form of

13

internal energy [8,10]. The function may be divided into two part, one absorbing the radiation

14

energy and transform it to thermal energy, and the other delivering this thermal energy to a fluid

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flowing through the device. Solar collectors generally fall into two categories: non-concentrating

16

and concentrating ones. Non-concentrating collectors use the same area for solar interception and

17

absorption, while concentrating collectors use reflecting surface(s) to focus the solar radiation on

18

an absorbing part [2,11].

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Flat-plate solar collectors are non-concentrating thermal collectors with a simpler design as

20

compared with the concentrating collectors [2]. The main parts of a flat-plate solar collector are a

21

flat absorbing plate, working fluid, ducts, insulation layer and glazing cover(s). They are

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designed to supply a moderate temperature difference up to 100 K. The major applications of

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MW energy where only a

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% is received by earth [1]. However, it is estimated that 30 minutes

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these collectors are water and building heating, air conditioning and industrial process heating

2

[12].

3

The success and improvement of these units depend on the accurate performance of each part. In

4

a theoretical analysis, Hellstrom et al. [13] have investigated the influence of optical properties

5

on the annual performance of flat-plate collectors. They have studied the installation of second

6

Teflon film glazing and Teflon honeycomb and reported an increase in the annual performance

7

of up to 5.6% and 12.1%, respectively. They have also claimed that a combination of these two

8

together with antireflection treated glazing leads to lower reflection and better absorptance. In

9

some other research works, the function of an absorbing surface and the manufacturing processes

10

have been investigated [14,15]. Whilst the optical absorption of flat-plate collectors has been

11

variously investigated, the other part of transferring thermal energy to the fluid has been a

12

subject for research works. Ho et al. [16] have experimentally and theoretically investigated the

13

use of double pass channel in a flap-plate collector. Their results indicate that the efficiency

14

improvement of the device with an external recycle is 28-95% as compared with a sub-collector

15

configuration. In another study, Ravi Kumar and Reddy [17] have numerically inspected the

16

insertion of porous disks in the fluid passage. They have claimed an increase of 64% in the

17

Nusselt number for the thermal performance, while the pressure drop increases in comparison

18

with the tubular receiver. They have also optimized the direction and size of the porous disk in

19

the tube. Ackermann et al. [18] have computationally investigated the effect of internal

20

longitudinal corrugated fins between parallel panel walls in laminar fluid flow regarding a flat-

21

plate solar collector. They have concluded that the overall performance increases as the pitch of

22

the fins decreases. Amongst the new studies, some have considered employing fluids with

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modified properties as the working fluid of the collector. Utilization of the nanofluids lies in that

2

category.

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A nanofluid is a suspension of solid particles with characteristic size of less than 100 nm

4

dispersed in a base fluid [19]. Experimental studies attest the enhancement of convective heat

5

transfer and thermal conductivity of nanofluids [20–22]. Pak and Cho [23] have experimentally

6

investigated the heat transfer and pressure drop of the Al2O3/water and TiO2/water nanofluids in

7

turbulent flow regime. Their results show an increase of 10% in thermal conductivity of

8

TiO2/water nanofluid for a 3.16% volume fraction. The experiment also reveals an increase of

9

approximately 45% in the convective heat transfer coefficient for the nanofluid. This

10

enhancement is more noticeable at higher volume fractions and mass flow rates. Parallel to the

11

experimental works, numerical modeling and simulations have been used to detect the flow and

12

thermal mechanisms corresponding to the heat transfer of nanofluids. Bazdidi-Tehrani et al. [24]

13

have investigated the laminar mixed convection of TiO2/water and CuO/water nanofluids inside

14

a rectangular vertical channel. They have employed the single- and two-phase approaches to

15

model the nanofluid behavior. Their results indicate that the two-phase model predicts the

16

convective heat transfer more accurately. In another study, Bazdidi-Tehrani et al. [25] have

17

numerically investigated the turbulent mixed convection flow of CuO/water and SiO2/water

18

nanofluids in a square vertical channel. They have used the scale-adaptive simulation (SAS)

19

approach in modeling the turbulence and single-phase approach for the nanofluid. Their results

20

show that the SAS approach delivers more accuracy in the simulation results of nanofluids

21

turbulent convection heat transfer, as compared with the

22

They have also concluded that the presence of nanoparticles increases the turbulent content of

23

flow field near the wall resulting in higher heat transfer.

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-based models (

and

).

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In the field of nanofluid application in the solar collectors both optical and thermal properties

2

have been investigated [10] . Jabari Moghadam et al. [26] have experimentally investigated the

3

effect of nanofluid on the efficiency of a flat-plate solar collector. They have employed

4

CuO/water nanofluid at 0.4% volume fraction with nanoparticles of size 40nm as the working

5

fluid. By variation of the nanofluid mass flow rate from 1 to 3 kg/min, their results show an

6

increase in efficiency in comparison with the water as the transport medium. For instance, the

7

nanofluid with a mass flow rate of 1 kg/min increases the efficiency up to 21.8%. Their

8

measurements also reveal the optimum mass flow rate for any particular working fluid which

9

maximizes the collector efficiency. In another experimental study, Sardarabadi et al. [27] have

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inspected the thermal and electrical efficiencies of a photovoltaic thermal unit (PV/T) with

11

SiO2/water nanofluid. They have measured the thermal and overall efficiencies of the unit and

12

reported a maximum increase of 12.8% and 7.9% for thermal and overall efficiencies,

13

respectively. Yousefi et al. [28] have experimentally investigated the influence of Al2O3/water

14

nanofluid in a flat-plate solar collector. They have used a commercial solar collector unit with

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nanoparticles of 15 nm in size at two weight fractions of 0.2% and 0.4%. Along with the use of a

16

surfactant, their results indicate 28.3% increase in the collector efficiency which is caused by the

17

enhancement in convective heat transfer. Jouybari et al. [29] have experimentally investigated

18

the effect of SiO2/water nanofluid in a flat-plate solar collector with channels filled with a porous

19

foam. They have considered nanoparticles volume fractions in the range 0.2% to 0.6%. Their

20

results indicate that thermal efficiency improves by up to 81% with the nanofluid flowing in the

21

porous medium. On the other hand, they have reported an undesirable pressure drop increase due

22

to the porous foam. Accordingly, they have concluded that a lower flow rate with a higher

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volume fraction of nanoparticles delivers a more efficient overall performance. Sundar et al. [30]

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have experimentally studied the effect of employing Al2O3/water nanofluid in a solar water

2

heater as well as inserting a twisted tape in the tubes. Their flow regime has been considered

3

turbulent with nanoparticles volume fraction of 0.1% and 0.3%. Their results show an increase of

4

21% in the thermal efficiency for using nanofluid whilst an increase of 28.7% occurs when

5

twisted tapes are inserted. They have also reported a maximum available efficiency of 76% at the

6

highest flow rate and nanoparticles volume fraction. In an analytical study, Mahian et al. [31]

7

have inspected the heat transfer, pressure drop and entropy generation in a flat-plate solar

8

collector with nanofluid. They have used SiO2/water nanofluid at 1% volume fraction with two

9

nanoparticle sizes of 12nm and 16nm. Their results show that higher heat transfer coefficient and

10

thermal efficiencies are achieved for nanofluid. They have also claimed that the use of nanofluid

11

decreases the entropy generation and increases the outlet temperature of the collector. Tyagi et

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al. [32] have theoretically and numerically studied the feasibility and performance of nanofluid

13

of water and aluminum particles in a non-concentrating low-temperature direct absorber solar

14

collector. They have modeled a two dimensional thin film of flowing nanofluid exposed to direct

15

sunlight. The results display that the absorption of incident radiation is enhanced by more than 9

16

times relative to that of pure water and the overall efficiency is improved by 10%. In a numerical

17

study, Nasrin et al. [33] have investigated the effect of nanofluids Prandtl number on the free

18

convection in a solar collector. Their geometry consists of a glass cover at top and dark colored

19

wavelike absorber plate at the bottom which is filled with working fluid. They have employed

20

Al2O3/water nanofluid with a volume fraction of 5%. Their results depict an enhanced

21

performance of heat transfer rate at a higher Prandtl number. This enhancement is more

22

prominent for Al2O3/water nanofluid than the base fluid. In another work, Bianco et al. [34] have

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numerically studied the potential application of Al2O3 nanofluid within a Photovoltaic/Thermal

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(PV/T) solar collector panel in order to improve the performance of the device. They have

2

considered the laminar forced convection flow of nanofluid with a range of nanoparticles volume

3

fraction of up to 6% in an asymmetric heated channel. They have also used a finite element

4

numerical approach in a two-dimensional simulation of the flow and heat transfer. Their results

5

indicate an improvement in the cooling performance with a top wall temperature reduction of up

6

to 5

7

significant reduction in the thermal entropy generation.

8

According to the literature review above, although various efforts have been made concerning

9

the augmentation of solar collector performance, there are still more tactics to achieve this

10

objective. The existing research works have been fixed at employing the regular plain ducts as

11

the flow passage geometry. In order to gain the most out of solar energy, the duct geometry and

12

flow conditions can be modified. In this regard, the ribbed duct along with the application of the

13

nanofluid is proposed in the flat-plate solar collectors.

14

In the present paper, the turbulent flow and heat transfer characteristics of TiO2/water nanofluid

15

through a ribbed flat-plate solar collector is investigated numerically. A three-dimensional

16

simulation of solid flat-plate with flow through the plain and ribbed ducts has been performed.

17

The scale-adaptive-simulation (

18

temperature fluctuations. The present results are directly compared with and validated against the

19

available experimental data of Pak and Cho [23]. The streamlines, velocity and temperature

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distributions of TiO2/water nanofluid at different Re and

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of the presence of the duct's ribs on the flow field. Moreover, the efficiency of flat-plate solar

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as well as an enhanced heat transfer coefficient of up to 15%. They have also reported a

) approach has been employed to simulate the velocity and

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are studied so as to find the influence

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collector is investigated for the plain and ribbed ducts at different

and . For a better

2

perception of the effect of different nanoparticles, the results of another nanofluid (CuO/water)

3

are additionally investigated in terms of the efficiency of flat-plate solar collector. Furthermore,

4

the influence of laminar and turbulent flow regimes on the thermal efficiency is considered for

5

both nanofluids.

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2. Mathematical Modeling

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2.1. Governing Equations

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The governing equations comprising the continuity, momentum and energy are formulated for

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the turbulent convection. Assumptions of incompressible flow and three-dimensional flow

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domain are taken into account [35]:

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(2)

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(1)

(3)

where,

(4)

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Considering the Reynolds averaging procedure, the instantaneous variables in the turbulent flow

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are decomposed into mean and fluctuating components:

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(5) (6)

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With these assumptions, equations (1) to (3) are rewritten as:

(8)

(9)

where,

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method employs the Boussinesq hypothesis [36] to relate the Reynolds stresses to the mean

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velocity gradients:

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and

are to be evaluated to close the governing equations. A common

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and

(7)

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(10)

(11)

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Concerning the evaluation of

, numerous models in the form of zero- to two-equation models

2

(i.e.,

3

the two-equation models is the lack of an underlying exact transport equation. Consequently, the

4

dissipation rate equations are heuristically suggested in analogy with the turbulence kinetic

5

energy. Rotta [37] has attempted a more consistent approach in formulating a scale equation. His

6

formulated transport equation of turbulence kinetic energy versus length scale has then been used

7

by Menter and Egorov [38]. They have proposed the Scale-Adaptive Simulation (

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Unlike

9

retaining the adopted length scale over the time, beneficially captures the resolved structures in

) approach.

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-based models) have been proposed. Generally speaking, the common problem of all

-based models which damp out any resolved structures, this approach, due to

10

the unsteady regions.

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In order to estimate the value of

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specific dissipation rate in the following transport equations. The transport equation of the

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turbulence kinetic energy is written as:

approach employs the turbulence kinetic energy and

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(12)

and the specific dissipation rate is given by the following equation: (13)

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where,

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calculated as follows:

where,

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represents the turbulence kinetic energy production term. The value of

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In equation (15),

is the distance to the next surface and

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cross-diffusion term of equation (14):

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In equations (12) and (13),

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obtained as follows:

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and

,

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The

(14)

(15)

is the positive portion of the

(16)

, and

are model constants which may be

(17)

model constants are listed in Table 1.

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is

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In equation (13), the term,

, is defined as:

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(18)

2

,

and

4

is calculated by:

are model constants (see Table 1). In equation (18),

In equation (18),

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the second derivative of the velocity vector [39,40]:

(21)

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where,

(20)

. The first and second derivatives of the velocity vector are obtained by:

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where,

(19)

is von Karman length scale and is defined as the ratio of the first divided by

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is the length scale and

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where,

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(22)

is the strain rate tensor and is computed by:

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(23)

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Table 1 The SAS approach constants [38]

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2.2. Nanofluid properties

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The single-phase approach is used to explicate the thermal and fluid dynamics characteristics of

6

the nanofluids. The inherent assumption of this approach is to consider the nanoparticles and

7

base fluid in a thermal equilibrium so that the suspension acts as a normal fluid. The fluid

8

properties are then assumed to be modified due to the inclusion of nanoparticles. With these

9

assumptions the critical aspect of the single-phase approach is to determine the effective thermo-

10

physical properties of the nanofluid. As the nature of the nanofluid is two-phase, it is desired to

11

consider the effects of internal interactions in the single-phase modeling of nanofluids. Despite

12

experimental measurements, different models and correlations have been proposed which are

13

based on the measurements and analytical techniques.

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The effective density and specific heat of the nanofluid in the single-phase approach are based on

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the classical theory of mixture and can be estimated using the following equations:

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(24)

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(25) These equations have originally been proposed by Pak and Cho [23] and then widely employed

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by different researchers [41–43].

3

In order to determine the effective thermal conductivity, the

4

estimate the thermal conductivity of the CuO/water nanofluid. The effects of nanoparticles size

5

and volume fraction as well as properties of the base fluid and nanoparticles are considered in

6

this model. Also, the effect of Brownian motion of nanoparticles is taken into consideration as

7

well as the conventional static effect of the presence of nanoparticles, which results in a

8

temperature-dependent model. The following equations represent the model formulation:

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and

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where,

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model [44] is employed to

(26)

(27)

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(28)

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On the other hand, the application of the

model for TiO2/water nanofluid has not approved

12

yet. Therefore, the experimental measurements for the effective thermal conductivity of

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TiO2/water nanofluid presented by Pak and Cho [23] have been directly employed for each

2

volume fraction. Regarding the experimental data on which the model is based, the range of

3

application regarding the nanoparticles volume concentration is

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effective viscosity of TiO2/water nanofluid is estimated on the basis of equations (29-31) which

5

are extracted from the experimental results of Pak and Cho [23]:

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. On the other hand, the

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(29) (30) (31)

The same extraction is done for the effective viscosity of CuO/water nanofluid based on the

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experimental results of Nguyen et al. [45] in the form of the following equations:

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(33)

Furthermore in the equations above, the volume fraction of nanofluid, , is calculated as below:

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(32)

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(34)

2.3 Solar radiation

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The useful energy gain (i.e., the amount of energy that can be delivered to the working fluid) of a

11

solar collector is calculated from the energy balance equation in the collector. Under the steady16

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state condition, the useful energy of a collector of area,

2

absorbed solar radiation and the thermal loss [12].

, is the difference between the

3

where

4

coefficient,

5

respectively.

6

In order to compute

7

the heat loss coefficient due to the radiative, convective and conductive energy losses to the

8

ambient. These losses depend on the number of glazing, emittance, wind speed, etc.

9

Computation of

are the mean plate temperature and the ambient temperature,

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and

is the collector overall heat loss

, there are graphs presented by Deceased and Beckman [12] representing

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depends on the beam and diffuse irradiation, and geometrical angles as well as

the radiative properties of the collector and earth. A simpler equation for

EP

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is the absorbed solar radiation per unit area,

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(35)

is as follows [12]:

(36)

where

is the average transmittance-absorptance product and

12

on the tilted surface of collector. The average product of transmittance-absorptance can be

13

evaluated using the approximation

14

beam radiation.

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is the measured irradiation

, where the subscript b denotes the

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1

For the thermal efficiency computation of the solar collector, the following equation is

2

employed:

3

where,

5

fluid.

is the mass flow rate through the collector and

represent the outlet and inlet temperatures of the fluid, respectively.

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and

is the specific heat of the working

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(37)

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3. Flow geometry and boundary conditions

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The turbulent convective flow of nanofluid through a ribbed square cross-section duct of a flat-

9

plate solar collector has been considered. The computational domain consists of two solid and

10

fluid parts representing the solid plate and nanofluid flowing domain, consecutively. The

11

geometry is adopted from a common design of the flat-Plate solar collectors [46]. As the

12

geometry of a solar collector is symmetrical about a duct axis, the domain is considered to be a

13

half of the distance between the two ducts. With this consideration, a half of the duct and plate

14

width has been included in the computation (see Figure 1). The solid plate of 20 cm width and 2

15

mm thickness is considered as the absorbing plate. A solid wall of the same thickness is assumed

16

as the duct wall containing a transverse square rib protruded into the fluid domain. The whole of

17

the solid part is presumed to be made of copper. For the fluid domain, a half of a square cross-

18

section duct of 2 cm width is considered. As a simplification, the whole length of the domain in

19

the flow direction contains one rib of 8 mm virtual pitch. In the other words, only an 8 mm

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portion of the collector length is simulated in the computational domain. The used pitch value

2

has been presented as the optimum value for the internal square ribs by Manca et al. [47]. The

3

periodic boundary condition is introduced at the inlet and outlet, and the symmetry boundary

4

condition at the faces parallel to the

5

conditions on the outer solid surfaces are heat fluxes of the net absorbed solar radiation and heat

6

loss to the bottom insulation. The ambient temperature is also assumed to be 30

7

condition is employed at the solid and fluid interfaces. It is also assumed that the nanoparticles

8

are spherical in shape with the same diameter of 27 mm. The size of other dimensions may be

9

found in Table 2.

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plane and at the end faces in the -direction. Boundary

Fig. 1 Schematic of geometry and boundary conditions

12

19

. The no-slip

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Table 2 Geometry and computational domain dimensions Fluid Domain Dimension

size 8

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Duct length in -direction

Duct height in -direction

20

10

Dimension Solid thickness Rib height ( -direction)

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Rib width ( -direction)

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Solid Domain

Rib pitch (virtual)

size

2

1

1

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Duct width in -direction

4. Numerical approach

4

The set of non-linear equations defined earlier in Section 3 is discretized using the finite volume

5

formulation introduced by Patankar [48] on a staggered grid. For the stability of the solution, the

6

diffusion term in the momentum equations is approximated by the second order upwind scheme.

7

Also, a power law scheme is adopted for the convective terms. For turbulent equations, the

8

second order upwind scheme is used for discretizing the convection and diffusion terms. The

9

SIMPLE algorithm [48] is employed to solve the coupled pressure-velocity equation. The

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transient formulation is set to be discretized by the bounded second order implicit method. A

2

value of

3

errors of the dependent variables of velocity and temperature are set at

4

In order to ensure that the present results are independent of the grid size, several different grid

5

distributions are examined. Also, the grid near the walls is fine enough to accurately capture the

6

wall effects. Since the low Reynolds number modeling of the turbulent flow is considered and no

7

wall function is employed, the first cell height in x- and y-directions must be placed in the

8

viscous sub-layer. Under this condition, the dimensionless wall distances,

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.

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s is considered for the time step size. The convergence criteria for the relative

and

are less than 10 [35]. In the present work, the first cell height in x- and y-

directions is taken as 0.000025 m for which

and

are computed to be 0.8 and 1.7,

11

respectively. Hence, with no application of any wall function, the flow field is simulated right

12

down to the walls. The growth rate of cell size is considered 1.05 to provide a smooth transition

13

in cell size and aspect ratio and deliver properly fine cells near the wall and the rib. Figure 2

14

illustrates a cross sectional view of the generated mesh on a plane parallel to the flow direction.

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Fig. 2 Cross sectional veiw of the generted mesh

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Table 3 represents the results of the grid independence test procedure, based on the peripherally

4

averaged Nusselt number of water in the ribbed channel with the Reynolds number based on the

5

hydraulic diameter equal to 30,000. In the computation of

6

temperature is used.

TE D

the peripherally averaged wall

Table 3 Number of grid points and first cell height to wall

EP

7

AC C

Number of grid points in directions

Number of grid points in

Number of grid points in

directions

direction

Difference (%) (

)

40

40

40

241.037

16.48

45

40

40

243.851

15.51

60

45

60

268.524

6.96

4

80

60

80

286.924

0.59

5

95

60

80

288.628

-

1 2 3

8

22

ACCEPTED MANUSCRIPT

1

It is observed that by changing the number of grid points in the x direction from 80 to 95, there is

2

only a deviation of 0.59% in the Nusselt number. Therefore, it is concluded that a structured grid

3

distribution of

4

flow field and heat transfer processes correctly.

5

In order to validate the proposed numerical method, three sets of the numerical results are

6

evaluated. The numerical results are computed at the

7

compared with the available experimental results of Pak and Cho [23], in terms of the

8

peripherally averaged Nusselt number and friction factor. The uncertainties reported for the

9

experimental data are within

and

directions is appropriate enough to determine the

RI PT

,

ranging from 10,000 to 30,000 and

M AN U

SC

in the

[23]. The present simulation results are compared with

10

experiment for water (

) and the two other TiO2/water nanofluid volume fractions used in

11

the experiment (

12

for a circular tube. However, it has been shown by Kays et al. [49] that if the internal flow

13

regime is turbulent, regardless of the cross-sectional shape, the computed behaviors are alike

14

based on the hydraulic diameter. That is, the results of a circular tube are comparable with a duct

15

of square cross-section. Figure 3 illustrates a comparison between the present numerical and

16

existing experimental

17

nanoparticles volume fractions of

18

results are represented as

). The data of Pak and Cho [23] has been obtained

AC C

EP

TE D

and

, both at the same

. Comparisons are made at three different TiO2

(pure water),

and

. The numerical

on the vertical axis. The averaged deviations of the

23

ACCEPTED MANUSCRIPT

1

numerical results are estimated to be

2

of

3

Table 4 illustrates comparisons of the computed peripherally averaged friction factor and the

4

experimental results of the pure water and TiO2/water nanofluid (

5

The averaged deviations from the experimental results are

6

(

7

It is observed that the numerical results are in reasonably good agreement with the experiment.

8

Therefore, the present numerical procedure is capable of simulating reliably the turbulent

9

convection flow of nanofluid regarding both the flow field and heat transfer parts.

for the volume fractions

RI PT

, respectively.

, consecutively.

AC C

EP

TE D

M AN U

) and

and

and

), at different

and

SC

,

,

24

.

for water

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

1 2 3

Fig. 3 Comparison of present simulations and experimental data [23] for TiO2/water nanofluid: versus at three values of

5 6

TE D

4

Table 4 Comparison of present simulations and experimental data [23] concerning peripherally averaged friction factor for TiO2/water nanofluid

EP

Water (

AC C

Re

Nanofluid (

)

Relative

Relative

error (%)

error (%)

10000

0.033828

0.031458

7.00

0.033893

0.030481

10.06

15000

0.032516

0.028923

11.04

0.031935

0.02813

11.91

20000

0.027413

0.02678

2.30

0.026788

0.026365

1.57

25000

0.024065

0.025502

5.97

0.024072

0.024893

3.41

30000

0.022622

0.024597

8.730

0.022522

0.023706

5.25

7 25

ACCEPTED MANUSCRIPT

1

5. Results and discussion

2

The simulation results of turbulent forced convection of TiO2/water nanofluid are presented at

3

different nanoparticle volume fractions (

4

to

5

the

6

Figure 4 shows the velocity contours and streamlines of the TiO2/water nanofluid flow over the

7

rib in the ribbed duct, at different

8

height ( -direction) of the duct and parallel to

9

region in the downstream of the rib is captured at all

range from

RI PT

) and

. The effect of internal rib in the solar collector ducts is also investigated in terms of

M AN U

SC

and collector efficiency.

. The results are presented for the plane located at the mid

TE D

plane, at

. The wake circulation

. It can be seen that the circulation wake

region in the back of the rib is intensified at higher

11

region gets closer to the rib which leads to an enhancement in the convective heat transfer in the

12

region. On the other hand, increasing

13

smaller area of low speed which again increases the convective heat transfer.

. Moreover, with increasing

, the wake

causes the flow in the upstream of the rib to face a

AC C

EP

10

26

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

1 2

Fig. 4 Velocity contours and streamlines of TiO2/water nanofluid for ribbed duct at a) b) c) d) and e)

3 27

:

ACCEPTED MANUSCRIPT

1

Figure 5 illustrates the effect of the presence of the rib on the temperature contours of the

2

TiO2/water nanofluid at

. The distributions are plotted at a plane parallel to the

plane in the mid of the duct so that the duct centerline lies on the plane. The temperature

4

distributions of nanofluids of different nanoparticle volume fractions flowing in the ribbed duct

5

geometry are compared with the water flowing in the no-rib (plain) duct geometry. Figure 5-a

6

represents the pure water in the plain duct while Figures 4-b to 4-e correspond to the ribbed duct

7

at nanoparticles volume fractions of

8

flow bulk temperature in the ribbed duct is higher than the plain duct. Also, in the ribbed duct,

9

the bulk temperature of the nanofluid increases slightly with the volume fraction. As the rib

10

causes more mixing in the flow field (see Figure 4), the wall heat flux is capable of penetrating

11

more easily through the fluid flow leading to a higher bulk temperature. On the other hand, it is

12

observed that the ribbed duct maintains a lower temperature at the wall which itself increases

13

the

14

ribbed duct.

SC

TE D

M AN U

, respectively. The

fundamentally means an enhanced convective heat transfer through the

EP

. A higher

AC C

15

RI PT

3

28

1 2 3

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Fig. 5 Temperature contours at Re=20,000: a) water (plain duct), b) water (ribbed duct) c) TiO2/water =0.99% (ribbed duct) d ) TiO2/water =2.04% (ribbed duct) and e) TiO2/water =3.16% (ribbed duct)

4

29

ACCEPTED MANUSCRIPT

1

Variation of the

of the turbulent water flow with

in the ribbed and plain duct is depicted

2

in Figure 6.

3

For instance,

4

ribbed duct. This enhancement is due to the circulating wake region caused by the rib and mixing

5

in the downstream flow which then increases the heat removal from the wall (see Figure 4).

for the ribbed duct is higher than that of the plain duct by 50.77% on average.

is 102.3 which is increased to 164.7 for the

EP

TE D

M AN U

SC

RI PT

of the plain duct at

6

Fig. 6 Variation of Nusselt number of water with Re in plain and ribbed ducts

AC C

7 8 9

Figure 7 illustrates the variations of the

with

regarding the turbulent forced convection of

10

water and TiO2/water nanofluid in the ribbed duct, at different nanoparticles volume fraction

11

(

).

augments with an increase in the nanoparticles volume fraction. For

30

ACCEPTED MANUSCRIPT

1

example, at

,

to

2

increases

. An enhanced

for variation of volume fraction from

for the higher volume fractions is due to the higher

thermal energy transfer between the nanofluid layers, which accordingly results in a higher bulk

4

temperature (refer to Figure 5). Moreover the

5

is a result of more intense turbulence at higher Reynolds numbers.

RI PT

3

which

EP

TE D

M AN U

SC

increase is more noticeable at higher

6

8

9

Fig. 7 Variation of Nusselt number with

AC C

7

at different

(Ribbed duct)

In order to investigate the simultaneous effect of thermal and hydraulic performance, the

10

parameter,

, is introduced. In this ratio, the friction factor is considered to be to the power

11

of 2, so that its order is more comparable to the Nusselt number. Since

31

and friction factor are

ACCEPTED MANUSCRIPT

1

favorable and adverse factors, respectively, in the flow and heat transfer, a higher value of this

2

ratio means a more optimum condition in the flow and heat transfer of the nanofluid. Figure 8 represents the variations of

4

volume fractions. It is observed that the value of

. Although, both

and volume fraction

and

augment with , the

increment in the favorable

suppresses the undesirable . Therefore, the adverse effect of

friction factor does not inhibit the overall enhancement of the thermal-hydraulic performance.

8 9

AC C

EP

TE D

7

increases as

SC

6

rise. This increase is more noticeable at higher

for the TiO2/water nanofluid, at different

M AN U

5

with

RI PT

3

Fig. 8 Variations of

versus Re at different φ for TiO2/water nanofluid

10

The distributions of solar collector efficiency as a function of the TiO2 nanoparticles volume

11

fraction (

) is demonstrated in Figure 9 (a-e). The collector efficiency of the

32

ACCEPTED MANUSCRIPT

1

ribbed duct is also compared with that of the plain duct at different values of the Reynolds

2

number (

3

increase in the nanoparticles volume fraction. This is true for both the plain and ribbed ducts at

4

all

5

plain duct. This enhancement is justified as the convective heat transfer in the ribbed duct is

6

determined to be higher than that of the plain one (see Figure 6). In another word, a higher

7

convective heat transfer to the working fluid results in a greater outlet temperature which in turn

8

enhances the efficiency of the collector.

RI PT

). The efficiency is shown to be moderately enhanced with an

AC C

EP

TE D

M AN U

SC

. The efficiency of the ribbed duct is approximately 10% higher on average than that of the

33

4

Fig. 9 Solar collector efficiency as a function of TiO2 nanoparticles volume fraction in plain and ribbed ducts: a) b) c) d) and e)

AC C

1 2 3

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

5

Figure 10 illustrates the variation of solar collector efficiency with

6

nanoparticles volume fractions for both the ribbed and plain ducts. In particular, the efficiency of

7

pure water in the plain and ribbed ducts is compared with that of the TiO2/water nanofluid, at

34

at various TiO2

ACCEPTED MANUSCRIPT

1

different . The highest enhancement in the efficiency is achieved by the nanofluid flow in the

2

ribbed duct, at

3

in the efficiency, TiO2/water nanofluid reaches a value of 81% at

4

and

.

7 8

AC C

6

EP

TE D

M AN U

SC

5

. With a maximum enhancement of 12%

RI PT

, for the present range of

Fig. 10 Variation of solar collector efficiency with Reynolds number at various nanofluid for ribbed and plain ducts

of TiO2/water

9

Figure 11 depicts the comparison of solar collector efficiency for CuO/water and TiO2/water

10

nanofluids at different Re and volume fraction. The CuO/water nanofluid provides a higher

11

thermal efficiency at each value of Re and

12

increases and reaches the highest value of 89% for the CuO/water nanofluid at = 2.04%.

. This enhancement grows as the volume fraction

35

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

1

Fig. 11 Comparison of solar collector efficiency for CuO/water and TiO2/water nanofluids at different and φ for ribbed ducts

4

Moreover, in order to provide a better insight into the effect of the turbulence, the results of

5

turbulent and laminar flow regimes are tabulated in Table 5. This is carried out in terms of the

6

ratio of thermal efficiency with nanofluid in a ribbed duct to thermal efficiency with water in a

7

plain duct. It is observed that the ratio

8

turbulent flow regime than the laminar one. Whilst this ratio increases in the turbulent regime, it

9

decreases in the laminar regime with

10

Table 5 Comparison of the ratio

EP

AC C

11

TE D

2 3

regimes at different Re and

has a greater value in the

.

in laminar and turbulent flow for TiO2/water and CuO/water nanofluids

Nanofluid Laminar

Turbulent

36

ACCEPTED MANUSCRIPT

CuO/water

0.99 2.04 3.16 0.99 2.04

1.1101 1.1114 1.1127 1.1628 1.2047

1.0777 1.0741 1.0705 1.1005 1.1304

1.1183 1.1281 1.1372 1.1882 1.2416

1.1437 1.1528 1.1606 1.1907 1.2537

1.1407 1.1524 1.1634 1.1970 1.2627

1.1455 1.1544 1.1654 1.1975 1.2709

RI PT

TiO2/water

1

Conclusions

3

The turbulent forced convection of TiO2/water nanofluid through a ribbed flat-plate solar

4

collector is studied numerically. The scale-adaptive-simulation approach has been employed to

5

simulate the turbulent flow through the plain and ribbed ducts which are surrounded by solid

6

flat-plate. The simulation results are presented at different nanoparticle volume fractions and

7

Reynolds number. The main conclusions may be drawn as follows:

The circulation wake region in the back of the rib intensifies at higher

, which leads to

enhancement in convective heat transfer at the region.

9 10

M AN U

•

•

TE D

8

SC

2

The flow bulk temperature in the ribbed duct is higher than the plain duct. Also, in the ribbed duct, the bulk temperature of nanofluid increases slightly with the volume fraction.

12

As the rib causes more mixing in the flow field, the wall heat flux is capable of

13

penetrating more easily through the fluid flow leading to a higher bulk temperature. •

Therefore, the

15 16

The ribbed duct maintains a lower temperature at the wall which itself increases the

AC C

14

EP

11

•

.

for ribbed duct is higher than the plain duct.

The efficiency of flat-plate solar collector is moderately enhanced with an increase in the

17

nanoparticles volume fraction. This is true for both the plain and ribbed ducts at all

18

whereas the efficiency of the ribbed duct is approximately 10% higher on average than

37

,

ACCEPTED MANUSCRIPT

1

that of the plain duct. This enhancement varies for different nanofluid so that the

2

CuO/water nanofluid provides higher thermal efficiency than TiO2/water nanofluid.

RI PT

3

4

NOMENCLATURE

Specific heat (

SC

Solar collector surface ) )

M AN U

Particle diameter (

Hydraulic diameter ( )

Peripherally averaged friction Factor (=

))

Peripherally averaged Convective heat transfer coefficient (

Coordinate index

TE D

Irradiation on tilted surface

Turbulence kinetic energy (

EP

Duct length ( )

)

Length scale

Von Karman length scale

AC C

Mass flow rate (

)

Peripherally averaged Nusselt number (= Pressure (

)

)

Prandtl Number (=

)

Useful energy gain of solar collector ( ) Heat flux (Wm-2)

38

)(=

)

ACCEPTED MANUSCRIPT

Reynolds Averaged Navier Stokes Reynolds number based on hydraulic diameter(= Absorbed solar radiation per unit area (

)

)

RI PT

Strain rate tensor (

)

Scale-Adaptive Simulation Time ( )

SC

Temperature ( ) Peripherally averaged wall temperature (K) )

Mean velocity component (

)

Fluctuating velocity component ( First derivative of velocity vector (

M AN U

Velocity vector (

)

)

Second derivative of velocity vector (

Friction velocity (

)

TE D

Velocity along x, y, z (

)

)

Solar collector overall heat loss coefficient (

EP

Coordinate system

dimensionless wall distance in direction direction

AC C

dimensionless wall distance in Greek Symbols

Absorptance

Turbulent (eddy) thermal diffusivity (

)

Kronecker delta Dissipation rate (

)

Solar collector thermal efficiency

39

)

ACCEPTED MANUSCRIPT

Boltzmann constant (=

)

Thermal conductivity ( )

Turbulent (eddy) viscosity ( Density (

)

RI PT

Dynamic viscosity (

)

)

Transmittance )

SC

Kinematic viscosity ( Particle volume fraction

)

M AN U

Specific dissipation rate ( Subscripts Ambient Average Beam radiation

TE D

Base fluid Inlet Nanofluid

Particle

EP

Outlet

Plate mean

1

2

AC C

Water

40

ACCEPTED MANUSCRIPT

1 2

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RI PT

3

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