## 2 Materials and Methods  
In this study, a 2D model is developed in COMSOL Multiphysics 5.5, where the heat transfer module is used to implement surface-to-surface radiation. Figure 2a shows a schematic of a typical pack of multiple, orthogonally arranged Li-ion cells with equal spacing. In general, the interest here is to understand how radiative heat transfer may facilitate the propagation of thermal runaway from one cell to the other. While the general problem comprising a number of cells is considerably complicated, for simplicity, the radiative exchange between a cell and one of its neighbors is considered first. The problem of radiation-induced thermal runaway between two neighboring cells may be treated as a 2D radiation heat transfer problem between two equal cylinders, as shown in Figure 2b. Figure 2: Schematic of simulation geometry of (**a**) a common configuration of cylindrical pack (**b**) two equal cylinders with radius R and separation d.  
In order to understand how these two cells exchange heat radiatively, the general energy conservation equation is first written. Thermal conduction in the axial direction is ignored, since a typical cylindrical cell has a high aspect ratio. The transient differential equation that balances heat conduction in the axial and azimuthal directions as well as thermal runaway chemical heat release is given by:  
\[\rho c_{p}\frac{\partial T}{\partial t}=\frac{1}{r}\frac{\partial}{\partial r} \bigg{(}k_{r}r\frac{\partial T}{\partial r}\bigg{)}+\frac{1}{r^{2}}\frac{ \partial}{\partial\theta}\bigg{(}k_{\theta}\frac{\partial T}{\partial\theta} \bigg{)}+Q \tag{1}\]  
where \(t,r,\theta,\rho,c_{p},T,k_{r},k_{\theta}\), and \(Q\) are time, radial coordinate, angular coordinate, battery density, heat capacity, radial thermal conductivity, azimuthal thermal conductivity, and heat generation within the battery, respectively. Based on previous work [34], the values of thermophysical properties of a typical Li-ion cell are provided in Table 1. Considering the jellyroll-layered structure of a cylindrical cell, the azimuthal in-plane thermal conductivity is much higher compared to the out-of-plane radial thermal conductivity. As such, the limiting heat conduction that is essential for thermal runaway initiation is in the radial direction. For these considerations, the problem is simplified as a 2D limiting condition with both \(k_{r}\) and \(k_{\theta}\) having equal out-of-plane thermal conductivity. The heat generation term \(Q\) originates from four well-known semi-global thermal runaway chemical reactions [12]. These exothermic reactions include the solid-electrolyte-interface decomposition reaction, the anode-electrolyte reaction, the cathode-electrolyte reaction, and the electrolyte decomposition. The rates of these reactions depend on the battery material properties, thermal chemical parameters, and the battery temperature. The reaction model, frequency factor, and activation energy that describe the kinetics between the electrolyte and electrode materials have been previously obtained by fitting the experimental measurements from accelerating rate calorimetry (ARC) and differential scanning calorimetry (DSC) tests. Expressions for the chemical reaction rates and heat generation rates for these reactions are shown in Tables 2 and 3, with symbols and parameter values used here as in our previous work [35; 36]. The present model for LCO thermal runaway chemistry is capable of accounting for more complicated reaction models and other cathode chemistry. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter (Unit)** & **Value** \\ \hline Battery radius, \(R\) (mm) & 9 \\ Battery density, \(\rho\) (kg/m\({}^{3}\)) & 2060 \\ Heat capacity, \(c_{p}\) (J/kg\(\cdot\)K) & 1000 \\ Radial thermal conductivity, \(k\) (W/m\(\cdot\)K) & 0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model parameters in the thermal radiation model [34].