## 4 Results and Discussion
### Air-Cooling BTMS with Homogeneous AFHS  
The open-cell aluminium foam has many irregularly shaped fluid channels; when cooling air flows through these channels, the heat transfers between the air and the three-dimensional network structure under the action of forced convection. On the one hand, the complex three-dimensional network structure of aluminium foam enhances the nonlinear effect of fluid. On the other hand, the large specific surface area of the aluminium foam is also an important reason for its good heat transfer performance. In addition, the high thermal conductivity of aluminium is also one of the factors to improve the heat transfer capacity. As a carrier of rapid heat transfer, the solid skeleton of the aluminium foam with high thermal conductivity is conducive to the uniform temperature of the whole porous area, transferring the heat to the fluid as soon as possible and accelerating the heat transfer process. Figure 4 shows the pressure drop \(P_{d}\) versus mass flow rate \(q_{m}\) with different parameters of AFHS. In all cases, the increase of \(q_{m}\) led to the increase of \(P_{d}\). In addition, at the same  
Figure 3: Air-cooling BTMS without AFHS: (**a**) temperature distribution of battery at \(q_{m}\) = 10 gs\({}^{-1}\), (**b**) pressure drop, (**c**) average temperature, and (**d**) temperature difference. pore density, the poor permeability of the aluminium foam with lower porosity resulted in a higher \(P_{d}\). Moreover, pore density has a remarkable influence on \(P_{d}\), the aluminium foam with large pore density has more ligaments, and the surface area of the solid aluminum skeleton per unit volume is much larger than that of low pore density foam, resulting in more flow resistance. Therefore, under the approximate porosity, the 40 PPI aluminium foam produced a higher \(P_{d}\) than 10 and 20 PPI aluminium foam. Figure 5a,b show the temperature distribution of the battery at 5 gs\({}^{-1}\) of cooling air for 10 PPI AFHS with a porosity of 0.918 and 0.682, respectively. It can be seen that the temperature distribution trend was similar to the case that without using AFHS, the temperature of the battery gradually increased along the direction of air flow. However, the \(T_{av}\) of the battery was significantly lower than the case without AFHS. Figure 6 shows the average temperature \(T_{av}\) of the battery with different parameters of AFHS. At 5 gs\({}^{-1}\) of cooling air, the \(T_{av}\) of the battery with AFHS was below 34 \({}^{\circ}\)C, the temperature control ability was much better than that without AFHS. It can also be seen that at a constant mass flow rate \(q_{m}\) and PPI, the battery with large porosity of AFHS had a higher \(T_{av}\). That is because there are more pores in large porosity AFHS, so the effective convective heat transfer area per unit volume is smaller. In contrast, the effective convective heat transfer area per unit volume of low porosity AFHS was larger, and a better cooling effect was achieved in air forced convection. As a result, the battery with low porosity AFHS had a lower \(T_{av}\). When the AFHS had a similar porosity, the effect of PPI on the \(T_{av}\) was negligible at a constant \(q_{m}\). For example, when the \(q_{m}\) was 2 gs\({}^{-1}\), the \(T_{av}\) of the battery  
Figure 4: Pressure drop versus mass flow rate with different parameters of AFHS. Figure 5: Temperature distributions of battery: (**a**) 10 PPI aluminium foam with 0.918 porosity, (**b**) 10 PPI aluminium foam with 0.682 porosity. with 10 PPI and 0.918 porosity AFHS was 39.92 \({}^{\circ}\)C, while the \(T_{av}\) of battery with 20 PPI and 0.924 porosity AFHS was 39.87 \({}^{\circ}\)C.  
When the cooling air flows over the surface of the battery, it first takes away the heat upstream, so the cooling capacity decreases gradually along the flow direction, resulting in the downstream temperature always being higher than the upstream temperature. This is the main reason for the uneven temperature of the battery.