# Design and Optimization of Cooling Plate for Battery Module of an Electric Vehicle
## 4 Surrogate Model-Based Optimization  
Apart from the analysis of the main parameters of the lithium battery modules in the above section, the arrangement and geometric details of channels also had influence on the battery temperature and the cooling plate temperature. In this section, the channels in the cooling plate were further optimized by the surrogate model of the cooling plate in the workbench platform [28; 29]. The flow chart of optimization was illustrated in Figure 16.  
Geometric parameterization was carried out on a quarter of the cooling plate, as shown in Figure 17. L\({}_{1}\), L\({}_{2}\), L\({}_{3}\), H\({}_{1}\) and H\({}_{2}\) were the geometric parameters of the cooling plate and the range of the geometric parameters were tabulated in Table 8.  
In the surrogate model, only the cooling plate was considered. To obtain the thermal load on the plate surface, heat flux distribution in the fluent model on the plate surface was first calculated as shown in Figure 18, and then heat flux values were extracted for seven straight lines on the surface of the cooling plate facing the batteries, as illustrated in Figure 19. The extracted values of seven lines were curve fitted by quadratic polynomial and the fitted curves were shown in Figure 20. All the heat flux curves increased towards the center of the plate and reached peak values at Z = 0 mm. The peak value at X = \(-\)126 mm was greater than that at X = 126 mm because the temperature difference between the coolant and plate at inlet was greater than that at the outlet.  
Figure 14: Surface temperature distribution of the cooling plate.  
Figure 15: Battery temperature.  
Figure 19: Heat flux on the surface of the plate.  
Figure 20: Fitting curves of heat fluxes at different location.  
Figure 18: Line location for heat flux extraction.  
The heat flux obtained above was expressed in the following equations. These functions were written as User Defined Functions (UDF) files and interpreted as thermal boundary conditions in fluent.  
\[\mathrm{q_{flux(-126)}}=923.7+2.8Z-21171.1Z^{2} \tag{10}\]  
\[\mathrm{q_{flux(-108)}}=914.4-1.9Z-17800.7Z^{2} \tag{11}\]  
\[\mathrm{q_{flux(-54)}}  
The 2 \({}^{\circ}\)C temperature difference of the cooling plates was set as the constraint, and the minimum pressure drop was taken as the objective to optimize this model.  
Three candidate designs were obtained, and the optimal parameters were selected as shown in Table 9. The optimized size of the cooling plate was presented in Table 10. The pressure drops calculated was 3.2176 kPa and the maximum temperature of cooling plate was 26.99 \({}^{\circ}\)C. Comparing with the results, which were not optimized, the plate temperature difference and pressure drop were reduced by 5.24% and 16.88%, respectively.  
Figure 21: Sensitivity of parameters.  
Figure 22: L\({}_{2}\), L\({}_{3}\) and temperature surrogate model.  
The numerical model (Figure 9) was then rebuilt with the optimized parameters. Battery surface temperature distribution, the cooling plate temperature distribution and coolant pressure distribution were shown in Figures 24-26, respectively. It can be seen that the maximum temperature of the cooling plate was 26.9 \({}^{\circ}\)C and the pressure drop was 3.2 kPa. The errors were 0.33% and 0.55% in comparison with the surrogate model for the plate temperature difference and pressure drop, respectively.