## 5 Results and Discussion
### Sensitivity Analysis with Coolant Flow Rate and Ambient Temperature
When the ambient temperature is 5 \({}^{\circ}\)C, the temperature difference between battery cells in the serial design is as high as 5.25 \({}^{\circ}\)C, while in the parallel design, the temperature difference is close to 4 \({}^{\circ}\)C. Another noteworthy observation for the 5 \({}^{\circ}\)C ambient temperature is that the SOC variation among cells in the serial design reaches as high as 3%. This indicates the necessity for careful cell balancing during the subsequent charging process. As the ambient temperature rises, the temperature difference between cells becomes smaller, accompanied by a reduction in differences in SOC, OCV, and SOP between cells. Similar to the observations in Figure 13, as the ambient temperature increases, the differences between the serial and parallel designs in terms of SOC, OCV, and SOP variations become smaller. However, the inhomogeneity of cells in the serial design remains greater than that in the parallel design. Under lower  
Figure 14: Performance of the serial and parallel module designs with ambient temperature. (**a**) Battery maximum temperature, (**b**) Inverter maximum temperature, (**c**) Motor maximum temperature, (**d**) Cooling system efficiency, (**e**) Maximum temperature difference between cells, (**f**) Maximum SOC difference between cells, (**g**) Maximum OCV difference between cells, and (**h**) Maximum SOP difference between cells. ambient temperatures, the parallel design is advantageous. It ensures that variations in temperature across cells are minimised, staying closer to the 4 \({}^{\circ}\)C mark. This is a priority where the highest temperatures within the battery pack are less of a concern, and uniformity in cell temperature takes precedence to maintain battery performance and longevity. From Figures 12-14, it can be observed that the magnitudes of OCV and SOP differences are less than 1 millivolt and 30 milliwatts, respectively. In practical engineering, accurately detecting voltage differences at the millivolt level or power differences at the milliwatt level presents considerable challenges and is susceptible to measurement errors. As a result, discerning cell-to-cell variations in OCV and SOP at such minute scales becomes practically unattainable through experimental means. However, the proposed multi-scale model enables the prediction of potential cell inhomogeneity and its developmental trajectory, even within short time frames. The model's ability to capture small fractions of cell inhomogeneity goes beyond the limitations of experimental measurements and can provide insights for the development of active cell balancing strategies. In some operating conditions these become large enough to have an influence on cell performance either instantaneously (e.g., SOC, SOP) or over longer timescales (cell-cell temperature variation impacting differential ageing in the pack). In summary, the comparison between the serial and parallel thermal designs gives the following findings for the case study described:  
1. The serial design exhibits advantages at the component and system levels, resulting in a lower temperature of the whole battery pack and higher efficiency of the entire cooling system at the expense of slightly higher temperatures of the other powertrain components. Compared to the parallel design, the serial design is more effective in dissipating heat for the whole battery pack, but this improvement comes at the expense of slightly higher temperatures for the inverter and motor components. However, when considering the overall heat dissipation of all components, the serial design still leads to higher efficiency of the cooling system [39]. 2. The parallel design exhibits advantages at the cell level, significantly reducing cell-to-cell inhomogeneity and thus alleviating the burden on BMS in cell balancing. Throughout the entire riding process, the parallel design consistently outperforms the serial design in terms of cell-to-cell variation.