## 2 3D Modelling and Cooling Performance Indicators
### Air-Cooling BTMS Dimensions and Configurations  
To fix the overall heat generations, the total cell number of 45 was selected as a typical example in all designs. The 45 cells could be divided into 9 columns with 5 cells in each column, which could provide enough variation margins for the gradient vertical spacing designs (4 \(\times\) 3, 5 \(\times\) 3, and 6 \(\times\) 3 cell arrangement). The 45-cell pack could also be used as one of the basic unit modules for the commercial EV battery pack. Furthermore, considering the calculation cost and computer load, the 45-cell air-cooling BTMS has a reasonable simulation volume for the average desktop in the labs (it takes about 5 h for a complete simulation at each operating condition). The dimensions of all 7 designs are shown in Figure 1. Seven designs include three similar derivative designs in two groups and two sets of opposite flow direction simulations for Design 4. The three variations in each group are meant to be sufficient to reflect the cooling performances of different vertical spacings and uncover the optimal cell spacing values. The horizontal cell spacings in all 7 designs were 30 mm, which was decided based on previous relevant research [13; 14; 15]. Design 1 was the basic rectangular 5 \(\times\) 9 battery pack. Both its horizontal and vertical spacings are 30 mm. Based on Design 1, the vertical spacings of every column in Design 2 and 3 were increased to 31.5 mm and 33 mm, respectively, by an increment unit of 1.5 mm, which increased the total cell spacing widths (the sum of four cell centre distances) of Design 2 and 3 to 126 mm and 132 mm, respectively. The reason for choosing 1.5 mm as the increment unit of the vertical spacings was that both 126 mm and 132 mm could be divided roundly by 3 (4-cell column), 4 (5-cell column), and 5 (6-cell column) with at most one decimal for the gradient vertical spacing designs. Due to the symmetrical structure of Design 1, 2, and 3, the inlet and outlet configuration of these three designs is similar to what is shown in Figure 2: 5-cell-side inlet and 5-cell-side outlet. Designs 4-7 were based on the concept of uneven vertical spacings: three 4-cell columns, three 5-cell columns, and three 6-cell columns. Design 4 is unique due to its 4-cell-side inlet and 6-cell-side outlet configuration, as shown in Figure 2. Both Design 4 and 5 have the same vertical spacing: 40 mm for the 4-cell column, 30 mm for 5-cell column, and 24 mm for 6-cell column as shown in Figure 1. Opposite to Design 4, Design 5-7 are all 6-cell-side inlet and 4-cell-side  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Major Parameters** & **Values** \\ \hline Cell length (mm) & 66 \\ Cell diameter (mm) & 21 \\ Anode tab diameter (mm) & 21 \\ Anode tab height (mm) & 2 \\ Cathode tab diameter (mm) & 13 \\ Cathode tab height (mm) & 2 \\ Active material density (kg/m\({}^{3}\)) & 2092 \\ Active material Cp (specific heat) (J/kg-K) & 678 \\ Active material thermal conductivity (W/m-K) & 18.2 \\ Active material electrical conductivity (Siemens/m) & 3.541 \(\times\) 10\({}^{7}\) \\ Passive material density (kg/m\({}^{3}\)) & 8978 \\ Passive material Cp (specific heat) (J/kg-K) & 381 \\ Passive material thermal conductivity (W/m-K) & 387.6 \\ Passive material electrical conductivity (Siemens/m) & 1 \(\times\) 10\({}^{7}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Dimensions and parameters of the 21,700 cylindrical Lithium-ion battery cell in this study.  
outlet configurations as shown in Figure 2. Based on Design 5, the vertical spacings for the 4-cell column, 5-cell column, and 6-cell column of Design 6 and 7 are 42 and 44 mm, 31.5 and 33 mm, and 25.2 and 26.4 mm, respectively, as shown in Figure 1. According to the vertical spacing patterns of each design, Design 1-3 were collated as the Constant Vertical Spacing Group (CVSG) while Design 4-7 were collated as the Gradient Vertical Spacing Group (GVSG). Design 4 is unique in the GVSG since its inlet/outlet positions are opposite to the other three designs in the group.