## 4 Discussion  
### Error Analysis Between Analytical Solutions and Numerical Simulations  
First, the differences between the theoretical solution and numerical simulation in the temperature profiles for a single cell are discussed. As evaluation metrics, the difference in maximum temperature \(\Delta T_{max}\) and the difference in the time to reach the maximum temperature \(\Delta t_{Tmax}\) are introduced. \[\Delta T_{max}=\left(T_{max,SIM}-T_{max,Analyt}\right) \tag{32}\]  
\[\Delta t_{Tmax}=\left(t_{Tmax,SIM}-t_{Tmax,Analyt}\right) \tag{33}\]  
where \(T_{max,SIM}\), \(T_{max,Analyt}\) means the maximum temperature of the numerical simulation and analytical solution, respectively. \(t_{Tmax,SIM}\), \(t_{Tmax,Analyt}\) means the time to reach the maximum temperature of the numerical simulation and analytical solution, respectively. Figure 9a,b show the relationship between various external heating powers \(q_{heating}\) and \(\Delta T_{max}\), and \(q_{heating}\) and \(\Delta t_{Tmax}\), respectively. For \(q_{heating}\) below \(1.5\times 10^{5}\) (\(\mathrm{W/m^{3}}\)), no thermal decomposition reaction occurs, and both \(\Delta T_{max}\) and \(\Delta t_{Tmax}\) are close to zero. However, for \(q_{heating}\) values greater than this threshold, both \(\Delta T_{max}\) and \(\Delta t_{Tmax}\) increase sharply. As \(q_{heating}\) increases further, both values tend to decrease. This can be explained by the fact that for relatively large \(q_{heating}\) values, the cell heating rate increases, making the linear approximation of the thermal decomposition reaction more valid. Figure 9c,d plot \(\Delta T_{max}\) and \(\Delta t_{Tmax}\) for various latent heats of the thermal decomposition reaction (\(Q_{tot}\)). As \(Q_{tot}\) increases, \(\Delta T_{max}\) increases almost linearly, while \(\Delta t_{Tmax}\) decreases monotonically. This suggests that as \(Q_{tot}\) increases, the nonlinearity of the thermal decomposition reaction becomes more pronounced, leading to a greater divergence from the linear approximation used in the theoretical solution. Based on the above, it can be concluded that in a single cell,  
Figure 8: (**a**) Temperature profiles of multiple battery cells for both the theoretical solution and numerical simulation at \(K_{cell}\) = 0.05 (\(\mathrm{W/m\cdot K}\)). (**b**) Temperature profiles of multiple cells with tuned parameters in the theoretical solution. the theoretical solution exhibits better accuracy to the numerical simulation as the external heating power is larger and the latent heat of the thermal decomposition reaction is smaller. Next, the differences between the theoretical solution and numerical simulation temperature profiles for multiple cells are discussed using the metrics introduced for the single-cell case. Figure 10a,b show plots of \(\Delta T_{max}\) and \(\Delta t_{Tmax}\) for various inter-cell thermal conductivities \(K_{cell}\). The values of \(\Delta T_{max}\) fluctuate for both the central and adjacent cells. On the other hand, \(\Delta t_{Tmax}\) increases almost linearly with \(K_{cell}\) for the central cell, changing from negative to positive values around \(K_{cell}\) = 0.4 (i.e., the theoretical solution has an earlier onset of the thermal decomposition reaction than the numerical simulation). In the adjacent cells, \(\Delta t_{Tmax}\) decreases monotonically with \(K_{cell}\), indicating an increasing delay in the theoretical solution relative to the numerical simulation. Figure 10: Plots between thermal conductivity between cells’ \(K_{cell}\) and (**a**) \(\Delta T_{max}\) and (**b**) \(\Delta t_{Tmax}\). As described in Section 3.2.2, by adjusting the heat transfer coefficient \(h\) of the central cell and the temperature frequency \(f\), the temperature profile of the theoretical solution was made to closely align with the numerical simulation. Here, the effective heat transfer coefficient \(h_{\textit{eff}}\) of the central cell, corresponding to changes in the thermal conductivity \(K_{\text{cell}}\) between cells, is discussed qualitatively.