*3.2. Modeling Method*

A three-dimensional model was built in SpaceClaim18.2. The meshing operation and numerical simulation were processed in ansys18.2. In order not to consider the energy consumption too much, the fluid inlet speed is set to 1 m/s and it is maintained by a fan in all designs. This is the typical forced

convection mode. The method of forced convection improves the heat dissipation effect by increasing the heat transfer rate per unit time. Compared with natural convection, it consumes more energy but performs very well with respect to thermal management. The Reynolds number can be calculated by Equation (9). In these models, the distance between the battery and the wall is 10 mm. The gap in the battery center is 20 mm. The fluid cross section with the largest characteristic length exists in a rectangular plane of 2 × 490 mm. The max Reynolds number here is 406, which determines the laminar flow type in the simulation.

$$\text{Re} = \frac{\rho v d}{\mu} \tag{9}$$

where ρ and μ are fluid density and dynamic viscosity coefficient, and υ, *d* are the characteristic velocities and characteristic length of the flow field.

The results of the grid independence test are shown in Figure 4, which ensure that the subsequent simulation process is reliable. In Figure 4, once the number of grids reaches 359,370–389,048, the MaxT of the model remains constant, that is, when the number of grids is more than 359,370, the size of the nodes will not affect the calculation results and the grid will pass the independence test. In order to save computing costs, the number of grids is selected as 359,370.

**Figure 4.** Grid independence test based on the maximum temperature (MaxT) and temperature standard deviation (TSD).

To simulate the flow model in ANSYS and compare the results, some assumptions need to made, including:


In the process of battery heat generation, the energy of the battery conforms to the law of COE [25,26], that is, it satisfies Equation (10),

$$
\rho \mathbf{C}\_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial \mathbf{x}\_d} (k\_{\mathrm{xd}} \frac{\partial T}{\partial \mathbf{x}\_d}) + \frac{\partial}{\partial y\_d} (k\_{\mathrm{yd}} \frac{\partial T}{\partial y\_d}) + \frac{\partial}{\partial z\_d} (k\_{\mathrm{zd}} \frac{\partial T}{\partial z\_d}) + Q\_v \tag{10}
$$

where ρ refers to density of battery; *Cp* is equivalent to SHC; *T* refers to the battery temperature; *kxd*, *kyd*, and *kzd* represent the heat conductivity coefficient (HCC) in the *x*, *y*, and *z* directions, respectively; and *Qv* is a volumetric heat source of battery, which is the same as the heat generation rate.

The energy conservation equation (ECE) for coolant [8] is expressed by Equation (11):

$$
\rho\_{\rm co} \frac{\partial T\_{\rm co}}{\partial t} + \nabla (\rho\_{\rm co} \overrightarrow{\nu} \, T\_{\rm co}) = \nabla (\frac{k\_{\rm co}}{\mathbb{C}\_{\rm co}} \nabla T\_{\rm co}) \tag{11}
$$

The coolant in this study is air, so the variable ρ*co* refers to the density of air; *Cco* and *kco* are the SHC and TC of the air, respectively.

The velocity of air is about 1 m/s whose Mach number is far less than 0.3. So, the continuous equation of coolant (which here refers to air) is as shown in Equation (12)

$$
\overrightarrow{\nabla \nu} = 0 \tag{12}
$$

where ν is the velocity vector.

> The momentum conservation equation (MCE) is shown in Equation (13).

$$
\rho\_{\rm co} \frac{d\overrightarrow{\nu}}{dt} = -\nabla P + \mu \nabla^2 \overrightarrow{\nu} \tag{13}
$$

where *P* and μ are the static pressure and dynamic viscosity of the air, respectively.
