# Design and Optimization of Cooling Plate for Battery Module of an Electric Vehicle
## 2 Thermal Analysis of a Single Battery
The heat generation rate of the lithium battery at 2C discharge rate was 29, 359.953W/m\({}^{3}\). C-rate is the measurement of the charge and discharge current with respect to its nominal capacity. Considering the experimental environment and the boundary conditions of simulation, the Boussinesq hypothesis was used for the calculation: (1) The dissipation of fluid viscosity was neglected during the process of fluid flow; (2) except the fluid density, other thermal properties were constant with varying temperature; (3) for density, only the terms related to volume force in momentum equation were included and the temperature of 25 \({}^{\circ}\)C was used as the reference temperature for calculation. The thermal properties of the battery are shown in Table 2:  
The dimension of the battery is 131 mm \(\times\) 65 mm \(\times\) 16 mm, the positive and negative electrode columns were not included in the model. The simplified model of the battery was established by CATIA as shown in Figure 1b, the fluid field was created according to the cooling method in Ge's \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Name**} & **Density** & **Specific Heat Capacity** & **Thermal Conductivity** & **Viscosity** \\  & **(kg\(\cdot\)m\({}^{-3}\))** & **(J\(\cdot\)kg\({}^{-1}\)\(\cdot\)k\({}^{-1}\))** & **(W\(\cdot\)m\({}^{-1}\)\(\cdot\)k\({}^{-1}\))** & **(kg\(\cdot\)m\({}^{-1}\)\(\cdot\)s\({}^{-1}\))** \\ \hline Cell & 1958.7 & 733 & 0.9/2.7/2.7 & - \\ Air & 1.185 & 1005 & 0.0263 & 0.0000184 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Thermophysical parameters [25]. experiment [16], as shown in Figure 1c. In the analysis, the natural cooling process of the lithium battery was simulated at 2C discharge rate for a period of 1800 s. The temperature evolution was monitored and outputted at the end of each time step. The results of the cell surface temperature after 1800 s at 25 \({}^{\circ}\)C are shown in Figure 2. The maximum temperature was 325.8 K and located in the central area of the battery surface. Surface temperature decreased gradually to the periphery. The lowest temperature of the battery was 322.2 K at the four corners. The temperature difference of the whole battery surface was 3.6 K.  
The velocity streamline diagram of air in a natural convection condition surrounding the lithium battery is shown in Figure 3. It can be seen that air flew from boundaries of air domain to the surface of the batteries, and buoyancy increased with the increase of the temperature on the surface of the battery. The air velocity in the central region leaving the battery surface with the highest temperature was 0.1362 m/s. To verify the thermal model of the single battery, comparison with the experimental results in paper [25] was plotted in Figure 4. The surface temperature was measured by a K-type thermocouple during the experiment. During the discharging process, the temperature at the monitoring point gradually increased with time. The highest temperature in the experiment and numerical analysis were 53.84 \({}^{\circ}\)C and 51.39 \({}^{\circ}\)C, respectively, implying a difference within 5%. The reasons for this error  
Figure 1: (a) Battery cell; (b) cell geometry; (c) heat transfer model. Figure 2: Surface temperature. may result from the assumptions made in the simulation and the heat generation equation did not take into account the polarization heat, chemical reaction heat, and the electrode cap heat. The cell discharged at 25 \({}^{\circ}\)C without cooling, the maximum temperature can reach 53.84 \({}^{\circ}\)C, which was higher than the optimum operating temperature range of the battery. Because of the various usage conditions of the EV battery, high power discharge will occur inevitably. When power batteries are assembled in large quantities, the heat dissipation efficiency becomes low. To solve this problem, it is necessary to design a standard battery module and incorporate a cooling system to ensure the working environment temperature of batteries.