## 4 Results and Discussion
### Air-Cooling BTMS with Homogeneous AFHS
The \(T_{d}\) of the battery should be as small as possible to ensure safety and electrical performance. Figure 7 shows the \(T_{d}\) of the battery with different parameters of AFHS. It can be seen that the \(T_{d}\) of the battery with AFHS was negatively related to mass flow rate \(q_{m}\), that is, the \(T_{d}\) decreased with the increase of \(q_{m}\). It is worth noting that the \(T_{d}\) of the battery increased significantly with AFHS compared with that without AFHS. For LIB, the ideal \(T_{d}\) was less than 5 \({}^{\circ}\)C. However, the \(T_{d}\) of the battery was found to exceed 7 \({}^{\circ}\)C at \(q_{m}=2\) gs\({}^{-1}\). In all cases, at least 5 gs\({}^{-1}\) of cooling air is required to achieve \(T_{d}\) of below 5 \({}^{\circ}\)C.  
When the mass flow rate \(q_{m}\) and pore density of AFHS remain unchanged, the temperature difference \(T_{d}\) of the battery is also negatively related to the porosity of the AFHS, that is, the larger the porosity, the smaller the \(T_{d}\) of the battery, while the pore density of AFHS has barely any effect on the \(T_{d}\) of the battery. For example, at \(q_{m}=5\) gs\({}^{-1}\), the \(T_{d}\) of the battery is 4.39 \({}^{\circ}\)C when using AFHS with 10 PPI and 0.794 porosity, while the \(T_{d}\) of the battery with AFHS of 20 PPI and 0.774 porosity is 4.36 \({}^{\circ}\)C.  
Figure 8a shows the relationship between the temperature control coefficient \(\alpha\) and the pumping power \(\Omega\), the range of pumping power represents the power of the different systems maintaining the mass flow at 2 to 7 gs\({}^{-1}\). In all cases, the \(\alpha\) increased with the increase of the \(\Omega\), but it rose more slowly at a high pumping power. In addition, the \(\alpha\) of low porosity AFHS was slightly larger in the whole pumping power range, but more pumping power was needed to achieve the same \(\alpha\). Figure 8b shows variations in  
Figure 6: The average temperature of the battery with different parameters of AFHS: (**a**) 10 PPI aluminium foam; (**b**) 20 PPI aluminium foam; (**c**) 40 PPI aluminium foam. Figure 7: The temperature difference of the battery when using AFHS with different parameters: (**a**) 10 PPI aluminium foam; (**b**) 20 PPI aluminium foam; (**c**) 40 PPI aluminium foam. temperature uniformity coefficient \(\beta\) with the pumping power \(\Omega\) for various cases. Since the temperature difference was greater than 5 \({}^{\circ}\)C at low mass flow, the \(\beta\) was less than 0 at low pumping power. In the whole pumping power range, the \(\beta\) of high porosity AFHS was higher than that of low porosity AFHS, and less pumping power was needed to reach the same \(\beta\), which means that the battery temperature field uniformity with high porosity AFHS is better. Figure 9 shows the figure of merit (FOM) versus mass flow rate \(q_{m}\) when using the AFHS of different porosity and pore density. The results show that the FOM value was larger than 1 in all cases, which indicates the comprehensive convection performance of AFHS with different parameters was better than that without AFHS. When the pore density remained unchanged, the average surface heat transfer coefficient of the AFHS with larger porosity was smaller, while the accompanying pumping power was also smaller, which eventually led to a higher FOM. In addition, when the porosities were similar, the AFHS with larger PPI consumed more pumping power, resulting in a lower FOM. For all calculated parameters above 10 PPI and 0.918 porosity, AFHS had the highest FOM, indicating that it performed better than the others when considering heat convection and energy dissipation.