thermal measurements of nanofluid for battery thermal management

Journal Pre-proof Using of double distribution function LBM (DDF/LBM) and experimental rheological/thermal measurements of nanofluid for Battery thermal management Muhammad Aqeel Ashraf, Zhenling Liu, Dangquan Zhang, Narjes Nabipour, David Ross

PII:

S0255-2701(19)31206-1

DOI:

https://doi.org/10.1016/j.cep.2019.107796

Reference:

CEP 107796

To appear in:

Chemical Engineering and Processing - Process Intensification

Received Date:

25 September 2019

Revised Date:

17 December 2019

Accepted Date:

23 December 2019

Please cite this article as: Ashraf MA, Liu Z, Zhang D, Nabipour N, Ross D, Using of double distribution function LBM (DDF/LBM) and experimental rheological/thermal measurements of nanofluid for Battery thermal management, Chemical Engineering and Processing - Process Intensification (2019), doi: https://doi.org/10.1016/j.cep.2019.107796

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Using of double distribution function LBM (DDF/LBM) and experimental rheological/thermal measurements of nanofluid for Battery thermal management

Dangquan Zhang 1,* [email protected], Narjes Nabipour4,*

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Muhammad Aqeel Ashraf1,2 [email protected], Zhenling Liu3 [email protected],

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[email protected], David Ross5* [email protected]

School of Forestry, Henan Agricultural University, Zhengzhou 450002, China

2)

Department of Geology Faculty of Science, University of Malaya, 50603 Kuala Lumpur,

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1)

Malaysia

School of Management, Henan University of Technology, Zhengzhou 450001, China

4)

Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam

5)

Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX

*

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78712, United States

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3)

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Corresponding authors: (D. Zhang), (N. Nabipour), (D.Ross)

Other emails for submission:, Muhammad Aqeel Ashraf , Zhenling Liu)

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Graphical abstract

Highlights

Battery thermal management is carried out



Free convection flow and heat transfer are analyzed



Experimental rheological/thermal properties are measured



The second law analysis is employed

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

The lattice Boltzmann simulation is used

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

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Abstract

The growing demand of electric vehicles (EVs) attracts many researchers to work on the battery thermal management to maintain the temperature of battery package in the desired temperature. In this regard, the present work aims to use the numerical and experimental approaches in order

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to perform the battery thermal management. The lattice Boltzmann method is used to simulate

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the fluid flow and heat transfer during free convection in a rectangular cavity included with

seven battery cylinders. The battery package and battery are simplified with rectangular cavity

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and circle cylinder, respectively. The top and bottom walls are kept at constant cold temperature

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with three different configurations (Smooth, Jagged and Zigzag). In addition, the cavity is filled

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with SLG (Single Layer Graphene)/water nanofluid which the thermal conductivity and dynamic viscosity are measured experimentally using modern devices. Furthermore, the second law

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analysis is carried out in order to find the influence of governing parameters including Rayleigh number, nanoparticle concentration (??=0.2, 0.4, 0.6, 0.8 and 1.0 mg/ml) and configuration of cavity on the local/total entropy generation. The flow structure, temperature field, local maps of

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heat transfer irreversibility and fluid friction irreversibility, volumetric magnitude of total entropy generation and average Nusselt number are presented.

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Keywords: Battery thermal management; Natural convection; Nanofluid; Lattice Boltzmann method; Second law analysis

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1. Introduction

The free convection problem attracts many researchers due to various applications of free

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convection in the industrial applications such as solar collectors, double-pane window, passive

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cooling, thermal storage, cooling of electronic devices and so on [1-4]. The free convection flow

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and heat transfer has important role in the battery thermal management as well.

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There have been various types of BTM systems developed for EVs [5-7]. To date, most of the studies on BTM systems are focused on the development of active cooling systems in which the

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coolant is air. However, air cooling may not be sufficient if the battery pack is under stressful operating conditions or in a thermal abuse condition [5]. As a result, many researchers are employing the liquid as the cooling fluid [6]. In addition, many researchers have also conducted

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some studies on the phase change material (PCM) BTM system, and found that it performs better in terms of battery-pack compactness and temperature uniformity, while the PCMs alone are still insufficient for high heat fluxes due to the low thermal conductivity of the PCM [7]. On the other hand, the battery thermal management using natural convection phenomenon needs to be investigated more due to limited numbers of works in this area. 4

Obviously, battery thermal management is needed in order to cool the system and decrease temperature difference. Meanwhile, nanofluid has been proved to possess an excellent ability to enhance heat transfer [8]. With the addition of nanoparticles, the heat transfer rate of original fluid can be increased with the enhanced thermal conductivity [9]. As early as 1995, Choi et al.

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[10] proposed to add nanoparticles into fluid in order to increase its thermal conductivity. Since then, nanofluid has received extensive attention and application in various occasions, such as

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micro-channel heat sink [11, 12], heat pipe [13, 14], kinds of industrial heat exchangers [15] and

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so on. Specifically, in the experiments of Li and Xuan [16], the coefficient of convective heat

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transfer received an enhancement of 60 % with 2.0 vol. % Cu-water nanofluid compared with

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pure water. This revealed the excellent potential of nanofluid on increasing heat transfer. In addition, Wu and Rao [17] used Cu-water nanofluid in order to manage the temperature of a

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battery during natural convection phenomenon. For this purpose, they used numerical simulation using lattice Boltzmann method.

As explained above, the free convection problem has various applications in the industrial

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projects. In this regard, this phenomenon has been investigated in the cavities with different thermal/physical boundary condition, operating fluids, initial conditions, and numerical methods and so on. Czarnota and Wagner [18] performed a numerical three-dimensional simulation of turbulent natural convection and radiation in a cuboidal enclosure which is included by horizontal plates of finite thickness and with high and low conductivities. They found that the 5

uniformity of the temperature distribution at the interface enhances because of radiation when the plates with low conductivity are implanted. Furthermore, it was shown that the convective drop is smaller in regions where plumes detach than in those places where plumes fall on the interfaces. Vasiliev et al. [19] carried out some experiments using two experimental setups on

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turbulent Rayleigh-Benard natural convection within cubical enclosure included with adiabatic side walls. They showed that qualitative and quantitative characteristics of fluid flow are similar

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despite of technical differences in the experimental setups. Moreover, the results showed that

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quantitative changes of characteristics of large-scale flow are occurred as Rayleigh number and

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Prandtl number enhance. Malekshah and Salari [20] conducted several experiments to investigate

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the laminar natural convection in a three-dimensional cuboidal enclosure. They carried out the experiments for different liquid height aspect ratios (AR=0.5, 0.625, 0.75 and 0.875) and

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Rayleigh numbers (Ra=1.4×108, 2.79×108, 6.98×108 and 8.37×108). Also, they compared the experimental results with the obtained computational data at the same configuration of enclosure, aspect ratios of liquid and Rayleigh numbers. They observed that there is good agreement

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between the numerical and experimental results. Furthermore, they measured the temperature distribution at the fluid medium and surface of side heaters with PT100 and LM35 sensors, respectively. Kuznetsov and Neild [21] have investigated the natural convection boundary layer of nanofluid along a vertical plate. A new enhanced boundary condition for the volume fraction of nanoparticles at the surface of the wall has been proposed. Wang et al. [22] used a modern 6

numerical method (hybrid lattice Boltzmann-TVD) to simulate the natural convection in a partially heated cavity filled with different nanofluids using Buongiorno’s model. They showed that the heat transfer enhances continuously at low Rayleigh number, but the heat transfer enhancement has an optimal point with maximum heat transfer rate at high Rayleigh number.

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Furthermore, they reported that the average Nusselt number reduces with increasing of heater

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length.

The main purpose of the present work is investigation of free convection flow and heat transfer

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for application battery thermal management in a battery package. The lattice Boltzmann method

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is used for the numerical simulation, and the ghost fluid boundary method is employed to treat

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the curved boundary condition. The Rayleigh number (103 to 106), nanoparticle concentration of

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SLG/water nanofluid and configuration of side walls are the governing parameters.

2. Description of problem

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The present work aims to investigate the free convection flow and heat transfer for battery thermal management of the battery package. The battery package has rectangular configuration which its bottom and top walls have three different configurations including Smooth, Jagged and Zigzag and are maintained in cold temperature (TC). In addition, the cavity is included with seven circle cylinders acts as 42110 cylinder li-ion battery and filled with nanofluid. The 7

schematic of considered configuration, dimensions and thermal boundary conditions are depicted in Fig.1. The inner circle cylinders are subjected to constant positive and negative heat flux (𝑞 " ) (Neumann boundary condition) which simplifies the conducted heat energy from battery and

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refrigerant bodies in the battery package.

Thermal boundary conditions

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Dimensions

Figure 1. Graphical presentation of dimensions and thermal boundary conditions.

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The width and height of the cavity are shown with W and L, respectively; and the diameter of cylinders is represented by D. The cavity is filled with SLG/water nanofluid. The bottom and top walls have three different configurations including Smooth, Jagged and Zigzag, as shown in

Smooth

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Fig.2, with constant cold temperature (TC).

Jagged

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Zigzag

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Figure 2. Graphical presentation of consider configuration of cavities.

The following dimensionless parameters are defined to describe the problem effectively:

𝑢 , 𝑈

𝑣∗ =

𝑣 , 𝑈

𝑥∗ =

𝑥 , 𝑅

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𝑢∗ =

𝑦∗ =

𝑦 , 𝑅

𝑡∗ =

𝛼𝑏 𝑡 , 𝑅2

𝑇∗ =

𝜆𝑏 (𝑇 − 𝑇𝑎 ) 𝑞𝑅

Where 𝑢∗ and 𝑣 ∗ represent the non-dimensional velocities in 𝑥 and 𝑦 directions; respectively, 𝑥 ∗

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and 𝑦 ∗ show the dimensionless coordinates, respectively. The dimensionless time and temperature are represented with 𝑡 ∗ and 𝑇 ∗ .

Moreover, the Rayleigh number is calculated using following equation:

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𝑔𝛽𝑊 4 𝑞 𝑅𝑎 = 𝑘𝜈𝛼

(1)

Where 𝑔, 𝛽, 𝑘, 𝜈 and 𝛼 define the gravity acceleration, thermal expansion coefficient, thermal conductivity, dynamic viscosity and thermal diffusivity, respectively. Moreover, the Rayleigh

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number is calculated based on the width of cavity (𝑊) and exchanged heat energy from top wall

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(𝑞).

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In addition, the average Nusselt number is calculated as follows:

(2)

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3. Mathematical approach

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𝐿 𝜕𝑇 ∗ 𝑁𝑢𝐴𝑣𝑔 = ∫ ( ) 𝑑𝑦 𝜕𝑥 0

3.1. Governing equations

For the present simulation, the governing equations of mass, momentum and energy conservation

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are given as follows [23, 24]:

𝜕𝜌𝑓 + ∇. (𝜌𝑓 𝒖) = 0 𝜕𝑡

(3)

𝜕(𝜌𝑓 𝒖) + ∇. (𝜌𝑓 𝒖𝒖) = −∇𝑝 + ∇. (𝜇𝑓 ∇𝒖) + 𝑭 𝜕𝑡

(4)

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𝜕(𝜌𝑓 𝐶𝑝𝑓 𝑇) + ∇. (𝜌𝑓 𝐶𝑝 𝑓 𝑇𝒖) = ∇. (𝜆𝑓 ∇𝑇) 𝜕𝑡

(5)

Where 𝜌𝑓 shows the density of fluid, 𝜇𝑓 denotes the dynamic viscosity, 𝐶𝑝 𝑓 represents the specific heat capacity and 𝜆𝑓 is the specific thermal conductivity of fluid. Furthermore, 𝒖, 𝑇 and

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𝑡 show the velocity, temperature and time, respectively. The following assumptions are

2) The Boussinesq approximation is employed.

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3) The viscous dissipation of flow is neglected.

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1) The operating fluid is considered as incompressible.

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considered during the simulations:

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3.2. Lattice Boltzmann method

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In the present work, the double distribution functions (DDF), which are employed to simulate the flow and temperature fields, are used. The distribution functions are coupled with each other to simulate the fluid flow and heat transfer simultaneously. The related equations of density and

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energy distribution functions are defined as follows [17, 24, 25]:

𝑓𝑡 (𝑥 + 𝑒𝑡 ∆𝑡, 𝑡 + ∆𝑡) = 𝑓𝑡 (𝑥, 𝑡) −

1 1 [𝑓𝑡 (𝑥, 𝑡) − 𝑓𝑡𝑒𝑞 (𝑥, 𝑡)] + (1 − ) 𝐹 ∆𝑡 𝜏𝑓 2𝜏𝑓 𝑡

(6)

1 [𝑔𝑡 (𝑥, 𝑡) − 𝑔𝑡𝑒𝑞 (𝑥, 𝑡)] 𝜏𝑔

(7)

𝑔𝑡 (𝑥 + 𝑒𝑡 ∆𝑡, 𝑡 + ∆𝑡) = 𝑔𝑡 (𝑥, 𝑡) −

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Where 𝑓 and 𝑔 denote the density and energy distribution functions; respectively, e shows discrete velocity with subscript of 𝑖 representing the related discrete direction. Furthermore, the discrete body force is defined by 𝐹𝑖 , and the non-dimensional relaxation time of density and energy distributions are denoted by 𝜏𝑓 and 𝜏𝑔 , respectively. Moreover, the equilibrium

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distribution functions of density is shown by 𝑓𝑖𝑒𝑞 , and the equilibrium distribution function of

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energy is denoted by 𝑔𝑖𝑒𝑞 . The equilibrium distribution functions of density 𝑓𝑖𝑒𝑞 and energy 𝑔𝑖𝑒𝑞

𝒆𝒊 . 𝒖 (𝒆𝒊 . 𝒖) 𝑢2 = 𝜔𝑖 𝜌 [1 + 2 + − 2] 𝑐𝑠 2𝑐𝑠4 2𝑐𝑠

𝒆𝒊 . 𝒖 (𝒆𝒊 . 𝒖) 𝑢2 + − 2] 𝑐𝑠2 2𝑐𝑠4 2𝑐𝑠

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𝑔𝑖𝑒𝑞 = 𝜔𝑖 𝑇 [1 +

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𝑓𝑖

𝑒𝑞

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are calculated as follows:

(8)

(9)

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Where 𝜔𝑖 shows the weight coefficient in the direction of 𝑖, and lattice sound is denoted by 𝑐𝑠 . In the present work, the D2Q9 lattice model is employed which the related weight coefficients and

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discrete velocities are given as follows:

4 9 1 𝜔𝑖 = 9 1 {36

𝑖=0 𝑖 = 1, 2, 3, 4 𝑖 = 5, 6, 7, 8

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(10)

(0, 0)

𝜋 𝜋 (𝑖 − 1)] , 𝑠𝑖𝑛 [ (𝑖 − 1)]) 𝑐 (𝑐𝑜𝑠 [ 𝑒𝑖 = 2 2 𝜋 𝜋 √2𝑐 (𝑐𝑜𝑠 [ (2𝑖 − 1)] , 𝑠𝑖𝑛 [ (2𝑖 − 1)]) { 4 4

𝑖=0 𝑖 = 1, 2, 3, 4

(11)

𝑖 = 5, 6, 7, 8

Where 𝑐 denotes the lattice speed and is calculated by ∆𝑥⁄∆𝑡. In addition, the external force 𝐹𝑖 in

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(12)

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𝒆𝒊 − 𝒖 𝒆𝒊 . 𝒖 𝐹𝑖 = 𝜔𝑖 ( 2 + 4 𝒆𝒊 ) . 𝑭 𝑐𝑠 𝑐𝑠

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Eq. (4) is given as follows:

Where 𝑭 shows the body force applied by fluid as a result of buoyancy force. In this regard,

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based on the Boussinesq approximation, the external body force can be calculated as follows:

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𝑭 = 𝜌𝒈𝛽(𝑇 − 𝑇𝑟𝑒𝑓 )

(13)

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Where 𝒈 represents the gravitational acceleration, 𝛽 shows the volumetric thermal expansion coefficient. Furthermore, the non-dimensional relaxation times for density and energy distribution functions 𝜏𝑓 and 𝜏𝑔 which are related on the properties of nanofluid are calculated as

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follows:

𝜏𝑓 =

𝜇 𝜈 + 0.5 = 2 + 0.5 2 𝜌𝑐𝑠 ∆𝑡 𝑐𝑠 ∆𝑡

𝑘 𝛼 𝜏𝑔 = + 0.5 = 2 + 0.5 2 𝜌𝐶𝑝 𝑐𝑠 ∆𝑡 𝑐𝑠 ∆𝑡

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(14)

Where 𝜈 and 𝛼 represent the kinetic viscosity and thermal diffusivity of operating fluid. Furthermore, the macroscopic variables can be calculated as follows: 8

𝜌 = ∑ 𝑓𝑖 0 8

𝜌𝒖 = ∑ 𝑒𝑖 𝑓𝑖

(15)

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0 8

𝑇 = ∑ 𝑔𝑖

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3.3. Boundary conditions of LBM for curved walls

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Since there are curved walls in the present problem, it is required to employ special treatments in lattice Boltzmann method. In this regard, an interpolation method which is named ghost fluid

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boundary condition and proposed by Khazaeli et al. [26], is utilized. A schematic presentation of

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the ghost fluid boundary condition is shown in Fig.3.

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Figure 3. Schematic of ghost fluid boundary condition

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The ghost fluid boundary can be described as follows:

The ghost points, which are represented by GPs and adjacent to curved boundaries, are required

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to be located. These points are important since they are dividing the computational field into

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fluid and solid domain. The image points, which are represented by IPs, describe the symmetry points and must be located like ghost points. It should be noted that the IPs are imaginary points which are required to achieve their interaction with ghost points. The following interpolation

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method is employed to provide the variable data of IPs: 4

𝛤𝐼𝑃 = ∑ 𝛿𝑘 𝛤𝑁𝑃𝑘 𝑘=1

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(16)

Where 𝛤𝐼𝑃 represents the major flow variables of an image point, and the major variables of the corresponding 𝑁𝑃𝑘 (𝑁𝑃𝑘 𝑤𝑖𝑡ℎ 𝑘 = 1, 2, 3, 4)are shown by 𝛤𝑁𝑃𝑘 . In addition, the interpolation coefficient 𝛿𝑘 is calculated as follows:

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1 1 𝛿𝑘 = 𝛽𝑘 2 (∑ 𝛽𝑘 2 ) 𝑑𝑘 𝑑𝑘

−1

(17)

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𝑘=1

Where 𝑑𝑘 defines the distance between 𝐼𝑃 and corresponding 𝑁𝑃𝑘 , and 𝛽𝑘 is defined as

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corrective factor in order to proceed the simulation when 𝑁𝑃𝑘 lies in the solid domain. In this

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regard, the magnitude of 𝑁𝑃𝑘 is set to 1 and 0 when 𝑁𝑃𝑘 located to fluid domain and solid

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domain, respectively. it is necessary to note that there is another situation which occurs when an image point IP is too close to a 𝑁𝑃𝑘 , which can be defined as 𝑑𝑘 ⁄√∆𝑥 2 + ∆𝑦 2 ≤ 10−6 as ∆𝑥

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and ∆𝑦 denote the horizontal and vertical grid distances, its related variables can be replaced by those corresponding variables of 𝑁𝑃𝑘 as follows:

(18)

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𝛤𝐼𝑃 = 𝛤𝑁𝑃𝑘

The physical (hydrodynamic) and thermal (heat transfer) boundary condition are needed to be imposed to image points (IPs) and corresponding ghost points (GPs) because the variables of image points (IPs) are provided. In this context, the interaction for the Neumann boundary condition can be described as follows: 16

𝛤𝐺𝑃 = 𝛤𝐼𝑃 − ∆𝑙 (

𝜕𝛤 ) 𝜕𝒏 𝐵𝐼

(19)

𝜕𝛤

Where 𝜕𝒏 calculated the gradient of major variables in the direction of normal vector which can be identified as heat flux in the present work since 𝛤 denotes the temperature. Nevertheless, the

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density of fluid at the ghost points GPs can be defined as follows:

𝜌𝐺𝑃 = 𝜌𝐼𝑃

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(20)

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A method developed by Tiwari et al. [27] is employed in order to divide the distribution

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functions into two discrete parts of equilibrium and non-equilibrium. This method helps us to

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estimate the unknown parameters at GPs including density and energy distribution functions. The equilibrium part is calculated by Eqs. (8) and (9) using derived variables by interpolation

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algorithm. Moreover, the non-equilibrium section can be approximated as the non-equilibrium function at corresponding IPs:

𝑓𝑡𝑛𝑒𝑞 (𝐺𝑃, 𝑡) = 𝑓𝑡𝑛𝑒𝑞 (𝐼𝑃, 𝑡)

(21)

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𝑔𝑡𝑛𝑒𝑞 (𝐺𝑃, 𝑡) = 𝑔𝑡𝑛𝑒𝑞 (𝐼𝑃, 𝑡)

Where 𝑓𝑖𝑛𝑒𝑞 = 𝑓𝑖 − 𝑓𝑖𝑒𝑞 and 𝑔𝑖𝑛𝑒𝑞 = 𝑔𝑖 − 𝑔𝑖𝑒𝑞 . Finally, with adding equilibrium and nonequilibrium parts, the distribution functions of density and energy are calculated as follows: 𝑓𝑖 (𝐺𝑃, 𝑡) = 𝑓𝑖𝑒𝑞 (𝐺𝑃, 𝑡) + 𝑓𝑖𝑛𝑒𝑞 (𝐺𝑃, 𝑡) 17

(22)

𝑔𝑖 (𝐺𝑃, 𝑡) = 𝑔𝑖𝑒𝑞 (𝐺𝑃, 𝑡) + 𝑔𝑖𝑛𝑒𝑞 (𝐺𝑃, 𝑡)

4. Nanofluid preparation

In the present work, the Single Layer Graphene (SLG) nanoparticles are added to pure water as

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based fluid in order to prepare the nanofluid. The SLG/water nanofluid is used as operating fluid.

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The density, specific heat capacity and volume expansion coefficient of nanofluid can be

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calculated as follows:

𝜌𝑓 = (1 − 𝜑)𝜌𝑤 + 𝜑𝜌𝑝

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(𝜌𝐶𝑝 )𝑓 = (1 − 𝜑)(𝜌𝐶𝑝 )𝑤 + 𝜑(𝜌𝐶𝑝 )𝑝

(23)

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(𝜌𝛽)𝑓 = (1 − 𝜑)(𝜌𝛽)𝑤 + 𝜑(𝜌𝛽)𝑝

Where the subscriptions of w and p denote the water and particle, respectively. In addition, the volume fraction of nanofluid is shown by 𝜑.

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4.1. Measurements of thermal conductivity and rheological properties

In order to prepare the SLG/Water nanofluid, the two-step method is employed. Four different samples of nanofluids with nanoparticle concentrations of 0.2, 0.4, 0.6, 0.8 and 1.0 mg/ml are provided. The thermal conductivity of nanofluid samples are measured using transient hot-wire

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method supported by a temperature controlled bath in the temperature range of 20 to 60 ℃. The temperatures of nanofluid sample and water bath are equalized in the period of 30 min, and the temperature of nanofluid samples are monitored for a period of 25 min. in addition, each measurements are taken at least 5 min. to measure the thermal conductivity of nanofluid samples,

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the KD2 Pro Thermal Properties Analyzer (Decagon devices, Inc., USA) is used, and the Brookfield viscometer of Brookfield engineering laboratories of USA is utilized for the

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measurements of viscosity.

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The transmission electron microscopy (TEM) micrograph of Single Layer Graphene (SLG)

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Nanoparticles is represented in Fig.4 in order to clarify the characteristics of SLG nanoparticles

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graphically. On the other hand, the thermo-physical properties of SLG nanoparticle, which is

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supplemented by US Research Nanomaterials, Inc., and base fluid are presented in Table. 1.

Figure 4. Transmission electron microscopy (TEM) images for SLG/water at 1wt% water dispersion (provided by US Nano Inc.).

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Table 1. Thermo-physical properties and characteristics of SLG nanoparticle Material

Purity (wt%)

Color

Size (nm)

Density (kg/m3)

Single Layer Graphene

99.3

Black

0.55-1.2

2267

Water

99.8

Colorless

-

998.8

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The provided samples of nanofluids at different nanoparticle concentrations (𝜑=0.2, 0.4, 0.6, 0.8 and 1 mg/ml) are presented in Fig.5. It should be noted that the samples are shown at two

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different times (3 days interval) in order to show the stability of samples. It is observed that no

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significant precipitations has been occurred at all nanoparticle concentration which declares the

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stability of samples and suggest that the SLG nanoparticles can be dispersed in pure water for a long time. It is due to the few residual hydrophilic groups such as hydroxyl, carboxyl, and

1.0 mg/ml

0.8 mg/ml

0.6 mg/ml

0.2 mg/ml

1.0 mg/ml

0.8 mg/ml

0.4 mg/ml

(b) After five days

ur na 0.6 mg/ml

0.4 mg/ml

Jo

0.2 mg/ml

(a) After preparation

lP

carbonyl group on the surface of graphene after the reduction process.

Figure 5. Samples of nanofluid at different nanoparticle concentrations (??=0.2, 0.4, 0.6, 0.8 and 1.0 mg/ml), (a) after preparation (left) and (b) after five days (right).

20

The magnitudes of dynamic viscosity are measured using prepared samples at different nanoparticle concentrations (𝜑=0, 0.2, 0.4, 0.6, 0.8 and 1 mg/ml) and in a range of temperature from 10 to 60 °C, as presented in Fig.6. It is observed that the nanoparticle concentration has increasing effect on the dynamic viscosity. Also, it is clear that the difference in dynamic

of

viscosity is greater and weaker in lower and higher temperature magnitudes, respectively. On the other hand, the temperature of nanofluid sample has a significant influence on the dynamic

ro

viscosity. It is seen that the reduction in the dynamic viscosity is occurred as the temperature

-p

enhances. Furthermore, there are linear reductions in the magnitude of dynamic viscosity at

Jo

ur na

lP

re

higher temperature which is due to weekend inter-particle and inter-molecular adhesion forces.

Figure 6. Dynamic viscosity based on temperature as a function of nanoparticle concentration.

The magnitudes of thermal conductivity are measured using prepared samples at different nanoparticle concentrations (𝜑=0, 0.2, 0.4, 0.6, 0.8 and 1 mg/ml) and in a range of temperature 21

from 10 to 60 °C, as presented in Fig.7. It is observed that the thermal conductivity of nanofluid samples enhances upon increasing of temperature magnitude. Similarly, the nanoparticle concentration has positive effect on the thermal conductivity of nanofluid samples in over the

lP

re

-p

ro

of

whole temperature range.

ur na

Figure 7. Thermal conductivity based on temperature as a function of nanoparticle concentration.

Based on the above-mentioned explanation, the thermo-physical properties of nanofluid samples including dynamic viscosity and thermal conductivity are measured experimentally. These

Jo

experimental results are used in the numerical simulations. It is worth noting that using of variable properties in the numerical process is neglected to simplify the numerical programming. For this purpose, the values of thermal conductivity and dynamic viscosity at 40 °C, which is considered as an average temperature, are used in the numerical simulations. As such, the

22

numerical process is repeated six times (for six nanoparticle concentrations) at each Rayleigh number and configuration of cavity.

5. Validation and grid independency analysis

In order to validate the numerical simulations, the present results are compared with a numerical

of

work carried out by Khazaeli et al. [28], as shown in Fig.8. They studied the natural convection

ro

heat transfer in the square cavity included with a circular cylinder subjected to a constant heat

-p

flux. The local dimensionless temperature at the surface of internal circular cylinder is compared at three different Rayleigh numbers (Ra=104, 105 and 106). It is seen that there are close

re

agreements between the numerical results at all Rayleigh numbers along the inner circular

lP

cylinder.

ur na

In addition, the grid independency analysis is performed to show that the numerical results are not relying on the mesh distribution, as shown in Table.2. In this regard, the magnitudes of average Nusselt number at five different mesh distributions at different configurations and

Jo

Ra=105 are compared. It is concluded that 360×360 is the best gird size based on the minimum error between the results.

23

Line……....Present work Symbol…..Khazaeli et al.

(𝑇 − 𝑇0 )⁄∆𝑇 ∗

104

ro

106

of

105

𝜃

re

-p

Figure 8. Comparison of local dimensionless temperature around the inner circular cylinder at four different Rayleigh numbers between present work and Khazaeli et al. [28].

Table 2. Grid independency analysis for different configurations and Ra=105 and 0.4 mg/ml.

260×260 310×310 360×360

Jagged

Zigzag

3.07

3.92

4.16

3.19

4.11

4.33

3.32

4.20

4.48

3.36

4.20

4.49

3.36

4.20

4.49

Jo

410×410

Smooth

ur na

210×210

Average Nusselt number (𝑵𝒖𝑨𝒗𝒈 )

lP

Rayleigh number

6. Results and discussion

24

The main purpose of the present investigation is the battery thermal management based on the thermal analysis of free convection phenomenon in the battery package. The rectangular cavity is a simplified battery package which includes four heat sources and three heat sinks acting batteries and refrigerants, respectively. The cavity is filled with nanofluid with experimental

of

thermo-physical properties. The flow structure, temperature distribution, heat transfer

concentration and configuration of cavity are presented.

ro

performance and entropy generation under influence of Rayleigh number, nanoparticle

-p

The contours of temperature field at different Rayleigh numbers (103, 104, 105 and 106), three

re

configurations (Smooth, Jagged and Zigzag) and 𝜑=0.4 mg/ml are shown in Fig.9. The

lP

temperature distribution within the computational domain can be observed using Fig.9. The isotherms have uniform patter in low Rayleigh number, but the pattern of isotherms changes to

ur na

wavy and non-uniform with increasing of Rayleigh number. It is due to changing of the regime of flow from laminar to turbulent. It should be noted that the non-uniform isotherms and flow structure causes higher magnitude of heat transfer coefficient.

Jo

Smooth

Jagged

Ra=103 Ra=104

25

Zigzag

Ra=105 Ra=106

-p

ro

of

Figure 9. Temperature fields at different Rayleigh numbers (103, 104, 105 and 106), three configurations (Smooth, Jagged and Zigzag) and ??=0.4 mg/ml.

re

The structures of flow fields at different Rayleigh numbers (103, 104, 105 and 106), three

lP

configurations (Smooth, Jagged and Zigzag) and 𝜑=0.4 mg/ml are shown in Fig.10. It is seen that the structure of nanofluid flow within the cavity is significantly complex because of inner

ur na

active cylinders. With increasing of Rayleigh number, the nanofluid flow is strengthened which can be realized by compacted streamlines within the computational domain. Moreover, the numbers of circulations in the cavity enhances as the Rayleigh number increases. Furthermore, it

Jo

is clear that the nanofluid structure has no considerable differences as the configuration of top and bottom walls is changed.

Smooth

Jagged

26

Zigzag

Ra=103 Ra=104

of

Ra=105

ro

Ra=106

re

-p

Figure10. Flow structures at different Rayleigh numbers (103, 104, 105 and 106) and configurations (Smooth, Jagged and Zi) and ??=0.4 mg/ml.

lP

The contours of heat transfer irreversibility and fluid friction irreversibility at Ra=104 and 𝜑=0.4 mg/ml are presented in Fig.11. Using contours of local heat transfer irreversibility and fluid

ur na

friction irreversibility, the regions which have main influence on the local and total entropy generation can be identified. It can be observed that the heat transfer irreversibility is maximum between the inner cylinders which is due to significant temperature gradients in these regions.

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This observation is repeated for all configurations. On the other hand, the magnitude of fluid friction irreversibility between the cylinders, where the nanofluid stream accelerates upwards, is significantly higher than other regions.

Heat transfer irreversibility

Fluid friction irreversibility

27

Smooth

Jagged

of

Zigzag

-p

ro

Figure11. Contours of heat transfer irreversibility (above) and fluid friction irreversibility (bottom) at Ra=104 and ??=0.4 mg/ml.

The average Nusselt number based on the nanoparticle concentration (0, 0.2, 0.4, 0.6, 0.8 and 1

re

mg/ml) and Rayleigh number (103, 104, 105 and 106) for different configurations of side walls are

lP

presented in Fig.12. The average Nusselt number is used as a criterion for determining the heat transfer performance under influence of different parameters. It is observed that the increasing of

ur na

Rayleigh number has considerable positive effect on the average Nusselt number. It is due to changing of regime of flow from laminar to turbulent as the Rayleigh number enhances. Similarly, adding nanoparticles to the base fluid causes improving of heat transfer performance

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which can be concluded by increasing of average Nusselt number. Finally, the maximum magnitude of average Nusselt number occurs in the cavity with Zigzag configuration.

Smooth

Jagged

28

-p

ro

of

Zigzag

re

Figure12. Average Nusselt number based on nanoparticle concentration and Rayleigh number for different configurations of side walls.

lP

The derived correlation of average Nusselt number based on the Rayleigh number for different

ur na

magnitudes of nanoparticle concentration and configurations of side walls are presented in Table.3. Using these correlations, the magnitude of average Nusselt number at all points in the

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range of 0-1 mg/ml and Ra=103-106 can be extracted exactly.

Table 3. Derived correlations based on Rayleigh number for different nanoparticle concentration and configurations of side walls. Correlation

Solid volume

Smooth

Jagged

Zigzag

NuAvg = 0.0423Ra 2 + 0.1636Ra

NuAvg = 0.0528Ra 2 + 0.2042Ra +

NuAvg = 0.0564Ra 2 + 0.2181Ra

fraction 0 mg/ml

29

0.4 mg/ml

0.6 mg/ml

0.8 mg/ml

1.5136

+ 1.6168

NuAvg = 0.0601Ra 2 + 0.2889Ra

NuAvg = 0.075Ra 2 + 0.3607Ra +

NuAvg = 0.0801Ra 2 + 0.3853Ra

+ 1.2196

1.5224

+ 1.6262

NuAvg = 0.1156Ra 2 + 0.3473Ra

NuAvg = 0.1443Ra 2 + 0.4335Ra +

NuAvg = 0.1541Ra 2 + 0.4631Ra

+ 1.4294

1.7842

+ 1.9059

NuAvg = 0.242Ra 2 + 0.3113Ra +

NuAvg = 0.302Ra 2 + 0.3886Ra +

NuAvg = 0.3226Ra 2 + 0.4151Ra

1.9481

2.4317

+ 2.5974

NuAvg = 0.3126Ra 2 + 0.7611Ra

NuAvg = 0.3902Ra 2 + 0.9501Ra +

NuAvg = 0.4168Ra 2 + 1.0148Ra

+ 2.4711

3.0845

+ 3.2948

2

NuAvg = 0.4682Ra + 1.5779Ra

NuAvg = 0.5844Ra + 1.9695Ra +

+ 3.6456

4.5506

NuAvg = 0.6243Ra 2 + 2.1038Ra + 4.8608

-p

ro

1 mg/ml

2

of

0.2 mg/ml

+ 1.2126

The total entropy generation based on the nanoparticle concentration (0, 0.2, 0.4, 0.6, 0.8 and 1

re

mg/ml) and Rayleigh number (103, 104, 105 and 106) for different configurations of side walls are

lP

presented in Fig.13. The magnitude of total entropy generation is based on the sum of the magnitude of heat transfer irreversibility (HTI) and fluid friction irreversibility (FFI). As can be

ur na

seen, the total entropy generation rises as the Rayleigh number enhances since magnitude of both HTI and FFI augment as a result of enhance temperature and velocity gradient, respectively. Reversely, the solid volume fraction of nanofluid has negative effect on the magnitude of total

Jo

entropy generation. It is due to the fact that the temperature gradient reduces as the thermal conductivity of nanofluid enhances, and the velocity gradient decreases as a result of increased dynamic viscosity.

Smooth

Jagged 30

-p

ro

of

Zigzag

lP

re

Figure13. Volumetric entropy generation based on nanoparticle concentration and Rayleigh number for different configurations of side walls.

The Bejan number based on the nanoparticle concentration (0, 0.2, 0.4, 0.6, 0.8 and 1 mg/ml) and

ur na

Rayleigh number (103, 104, 105 and 106) for different configurations of side walls are presented in Fig.14. The Bejan number is used in the second law analysis when it is desired to determine

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the share of heat transfer irreversibility and fluid friction irreversibility on the magnitude of total entropy generation. It can be observed that the magnitude of Bejan number reduces when the Rayleigh number increases since the magnitude of fluid friction irreversibility considerable increases. Similarly, the Bajan number has direct relationship with the nanoparticle concentration.

31

Jagged

of

Smooth

lP

re

-p

ro

Zigzag

ur na

Figure14. Bejan number based on nanoparticle concentration and Rayleigh number for different configurations of side walls.

7. Conclusions

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The main purpose of the present work is battery thermal management of a battery package during free convection. The thermal analysis of natural convection is performed using lattice Boltzmann method, and the curved boundaries are treated using ghost boundary approach. The cavity is filled with SLG/water nanofluid which its thermal conductivity and dynamic viscosity are measured experimentally using modern devices. The considered governing parameters in the 32

present work are Rayleigh number (103 to 106), solid volume fraction (0, 0.2, 0.4, 0.6, 0.8 and 1 mg/ml) and configurations of top and bottom walls. It is concluded that the Rayleigh number has remarkable effect on the heat transfer performance of battery package as the average Nusselt number enhances. On the other hand, the heat transfer performance of cavity is improved with

of

adding nanoparticles to the base fluid. The magnitude of total entropy generation increases reduces with increasing of Rayleigh number and solid volume fraction, respectively. In addition,

ro

it is observed that the best heat transfer performance occurs in the cavity with Zigzag

-p

configuration. On the other hand, the Rayleigh number has reducing effect on the value of Bejan

re

number. Although the effect of volume fraction of nanofluid on the Bejan number is minor with

lP

respect to the influence of Rayleigh number, the value of Bejan number is decreased with

Jo

ur na

increasing of volume fraction of nanofluid.

33

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35