## 4 Results and Discussion
### Air-Cooling BTMS with the AFHS of Gradient Porosity Designs
#### 4.3.2 AFHS with Gradient Porosity Designed in the \(X\)-Axis Direction (the Flow Direction)  
Figure 16 shows the pressure drop \(P_{d}\) of AFHS with gradient porosity designed in the \(X\)-axis direction (the air flow direction). At the same porosity levels, the pressure drop of AFHS with gradient porosity designed in the \(X\)-axis direction was not significantly different from that of homogeneous porosity AFHS. This means that the gradient porosity designed in the \(X\)-axis direction will not improve the flow performance of the AFHS. Figure 17a,b shows temperature distributions of battery with AFHS with gradient porosity designed in the \(X\)-axis direction. Figure 17c shows the \(T_{av}\) of the battery with AFHS with gradient porosity designed in the \(X\)-axis direction. It was found that at the same porosity level, whether using the AFHS of PIGP or PDGP, the \(T_{av}\) was almost unchanged, which was slightly higher than that with the equivalent homogeneous porosity AFHS, indicating the gradient porosity designed in the \(X\)-axis direction has no effect on reducing the \(T_{av}\). Figure 16: Pressure drop with AFHS with gradient porosity designed in the \(X\)-axis direction. Figure 15: FOM versus mass flow rate (with AFHS with gradient porosity designed in the \(Z\)-axis direction). To show the influence of gradient porosity designed along the flow direction on temperature difference \(T_{d}\) more directly, the \(T_{d}\) of the battery was divided into three figures according to the equivalent porosity level, which are shown in Figure 17d-f. Under the same porosity level, the battery with AFHS of PDGP had a smaller temperature difference, while with AFHS of PIGP had a larger temperature difference compared with the equivalent homogeneous porosity AFHS. During the cooling process, the cooling air shows the trend of increasing its temperature, which results in the upstream of the battery along the flow direction generally having a better cooling effect than the downstream. Therefore, the idea of reducing the battery temperature difference is to weaken the upstream heat transfer  
Figure 17: With AFHS with gradient porosity designed in the \(X\)-axis direction: (**a**) temperature distributions of battery with AFHS of PDGP m = 1; (**b**) temperature distributions of battery with AFHS of PIGP m = 1; (**c**) average surface temperature; (**d**) temperature difference of equivalent porosity = 0.9, (**e**) temperature difference of equivalent porosity = 0.8, and (**f**) temperature difference of equivalent porosity = 0.7.  
effect or strengthen the downstream heat transfer effect. Compared with the homogeneous porosity AFHS, when the porosity decreases along the flow direction, the upstream high porosity aluminum foam has more internal pores, and the effective heat transfer area per unit volume is smaller, thus weakening the heat transfer effect of the upstream of the battery. The low-porosity aluminum foam in the downstream has a larger effective heat transfer area, which strengthens the downstream heat transfer effect, so the temperature difference decreases. As the porosity increases along the flow direction, the upstream low-porosity aluminum foam has more convective heat transfer area, thereby enhancing the heat transfer effect in the upstream of the battery, while the downstream high porosity aluminium foam weakens the heat transfer effect, thus resulting in the increase of the temperature difference. Comparing the above three figures, it can also be found that using the AFHS of PDGP with m = 1, the lowest temperature difference was \(T_{d}\) = 3.1 \({}^{\circ}\)C at \(q_{m}\) = 7 gs\({}^{-1}\). Figure 18a shows temperature control coefficient \(\alpha\) with AFHS with gradient porosity designed in the \(Z\)-axis direction. Since the average temperature of battery and pressure drop under the same porosity level were almost identical, the temperature control coefficients \(\alpha\) were basically the same.