## 4 Optimization of Battery Pack Area Based on Stud Genetic Algorithm
### Result Analysis  
The initial condition was \(\theta_{\text{cp}}=15^{\circ}\), \(\theta_{\text{dp}}=15^{\circ}\), \(w_{\text{cp}}=5\) mm. After iterative calculation, the optimal solution was \(\theta_{\text{cp}}=14.0^{\circ}\), \(\theta_{\text{dp}}=10.1^{\circ}\), \(w_{\text{cp}}=10.2\) mm. The structure parameters and optimization results of various BTMSs are shown in Table 3. The stud GA-optimized  
Figure 14: Flow chart of battery pack optimization.  
BTMS was denoted as SG-opt. The BTMS optimized by sensitivity analysis was recorded as A-opt.  
The temperature of battery unit for various BTMSs calculated by the heat dissipation model is shown in Figure 15. Compared with A-opt1 and A-opt2, the original BTMS had a high \(T_{\text{max}}\) and a low \(T_{\text{min}}\), which made the maximum temperature difference greater than that of A-opt1 and A-opt2. The maximum temperature difference was 5.9 and 5.0 K for the original BTMS and stud GA-optimized BTMS, respectively. Furthermore, it also indicated that the temperature dropped overall after stud GA optimization. Compared with the original BTMS, not only did the maximum temperature difference decrease by 1.4 K but also the area of battery pack was reduced.  
The air velocity in each BTMS cooling channel is shown in Figure 16. It can be seen that the air velocities near the inlet were low. The faster the air velocity in the cooling channel, the more heat the air could take away, which caused the temperature of the battery unit near the inlet to be higher than the temperature of the battery unit near the outlet. Compared to A-opt1 and A-opt2, the minimum air velocity of the original BTMS is lower and the maximum air velocity was higher, which made the air velocity difference in original BTMS the largest, which in turn caused the maximum temperature difference to be the largest. Furthermore, the air velocity optimized by stud GA became higher overall so that the air took away more heat, making the temperature optimized by stud GA decline overall.  
The optimization result was then analyzed. As shown in Table 3, in the case that the maximal temperature difference was within 5K, the BTMS optimized by the stud GA saved 8.64% (A-opt1) and 8.46% (A-opt2) of the area, respectively. Compared with the original BTMS, the BTMS optimized by stud GA reduced the maximal temperature difference by 15.99% and reduced the area by 6.24%. Therefore, the stud genetic algorithm-optimized BTMS had a better heat dissipation effect than the original BTMS, which not only made the maximum temperature difference within 5K, but also saved more area.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**BTMS** & \(\theta_{\text{cp}}\) (\({}^{\circ}\)) & \(\theta_{\text{dp}}\) (\({}^{\circ}\)) & \(w_{cp}\) (mm) & \(\Delta T_{\text{max}}\) (K) & **Area (m\({}^{2}\))** \\ \hline origin & 15.0 & 15.0 & 5.0 & 5.9 & 1.7747 \(\times\) 10\({}^{-2}\) \\ A-opt1 & 17.1 & 15.0 & 5.0 & 5.0 & 1.8212 \(\times\) 10\({}^{-2}\) \\ A-opt2 & 15.0 & 15.0 & 7.8 & 5.0 & 1.8176 \(\times\) 10\({}^{-2}\) \\ SG-opt & 14.0 & 10.1 & 10.2 & 5.0 & 1.6639 \(\times\) 10\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison before and after optimization at inlet airflow rate of 0.040 m\({}^{3}\)/s.  
Figure 15: Comparison of the battery unit temperature before and after optimization.