## 5 Results and Discussion
### Cell-Level Analysis for the Base Case  
Figure 11 illustrates the transient performance (voltage and power) of the cells within two module designs at the middle of the riding time. The \(x\)-axis represents the cell numbers, consistent with Figure 8. Figure 11a indicates that the voltage of individual cells in the serial design increases from the upstream to the downstream of the coolant, but the rate of voltage rise decreases gradually, even though the voltage gradient of the cells exhibits a near-linear trend. Similarly, Figure 11b shows that, in the parallel design, the individual cell voltages in each parallel thermal circuit exhibit a similar trend, and the voltages across different parallel thermal circuits are very similar to each other. By comparing Figure 11a,b, it can be observed that the range of individual cell voltages in the serial design is larger than that in the parallel design, with a difference slightly greater than two times, although in absolute terms for this single drive cycle, this difference is negligible [38]. Figure 11c,d demonstrate \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Serial Module Design** & **Parallel Module Design** \\ \hline Battery efficiency & 94.76\% & 94.77\% \\ \hline Overall powertrain efficiency & 80.06\% & 80.07\% \\ \hline Equivalent energy consumption & 29.82 kWh/100 km & 29.81 kWh/100 km \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Energy efficiency with the serial and parallel module designs. that the power gradients across cells are highly nonlinear. The power of individual cells from the upstream to downstream of the coolant does not exhibit a monotonic trend but rather fluctuates. This observation holds true for both serial and parallel designs. However, in the serial design, the range of individual cell power is greater than that in the parallel design, slightly less than two times the difference. Figure 12 shows additional performances of cells within the serial and parallel module designs. Unlike the voltage and power shown in Figure 11, which are influenced by instantaneous current demands, the temperature, SOC, OCV, and SOP shown in Figure 12 are not affected by transient currents. Instead, they represent the cumulative states of the battery under longer-term drive cycle effects, making them more representative of the cells' overall condition. Additionally, Figure 12 not only shows the results at the middle of the riding time but also includes the results at the end of the riding time, providing a more comprehensive understanding of the cells' performance throughout the riding process. Figure 12a,e show the temperature gradients across cells in the module in the serial and parallel designs at the middle and end of the riding. The temperature differences among cells can be attributed to multiple factors. First, in the serial cooling design, the sequential heat absorption along the coolant flow path results in higher temperatures for downstream cells due to diminished cooling effectiveness. In contrast, the parallel design mitigates this effect by maintaining a more uniform coolant flow across the module. Second, the heat generation within individual cells varies due to differences in their SOC, internal resistance, and operating conditions, leading to non-uniform Joule heating. Lastly, environmental boundary effects, such as enhanced heat dissipation for edge cells compared to central cells, also contribute to the observed temperature gradients. It can be observed that, at the middle of riding, the temperature range of individual cells in the serial design is 0.45 degrees more than that of the parallel design, while at the end of riding, this difference expands to 1 degree. At the end of riding, the temperature differences between cells in the serial and parallel designs reached 4.34 \({}^{\circ}\)C and 3.34 \({}^{\circ}\)C, respectively. Throughout the entire riding process, the average temperature of cells in the serial design is lower than that of the parallel design.