## 3 Analysis of the EV Thermal Runaway Fire Scenarios
### Analysis of Thermal Radiation from an EV Fire and the Damage Caused
The flame radiation emission capacity is (\(\mathrm{kW/m^{2}}\)) \(E=\epsilon_{f}\sigma T^{4}\), where \(\epsilon_{f}\) is the radiant emissivity of the flame surface, \(\sigma\) is the Stephen Boltzmann constant (\(5.67\times 10^{-11}\)\(\mathrm{kW\cdot m^{-2}\cdot K^{-4}}\)) and \(T\) is the absolute temperature of the blackbody (K). The radiated heat flux received by the target depends mainly on the relative positions of the flame and target, size and shape of the flame and thermal radiation emission power of the flame. The heat released during the entire combustion process is transferred by conduction, convection and radiation. The proportion of the heat generated by combustion and transferred by thermal radiation was approximately 30-70% in the scenario experiments and statistical analyses of the experimental results [17, 37, 38]. We assumed that the heat transfer ratio \(X_{r}\) of the EV thermal runaway fire through the thermal radiation in the roadside parking scenario was 0.5 and \(A_{f}\) was the sum of all the luminous flame surfaces \(S_{lum}\) (excluding the bottom surface of the SFM) in the SFM, \(A_{f}=\sum S_{lum}\). The flame radiation emission capacity E is determined as follows:  
\[E=X_{r}.\frac{Q}{A_{f}} \tag{4}\]  
According to Equations (3) and (4), the calculation formula for the incident thermal radiation flux q can be obtained as follows [17, 34]:  
\[q=X_{r}.\frac{QF\tau_{air}}{A_{f}} \tag{5}\]  
According to Equations (1)-(5), the view factor F, based on the geometric relationship between the flame surface and the receptor target, is the key variable affecting the thermal radiation transfer. Calculation of the view factor based on the SFM  
Most flame radiation receptors (pedestrians, other vehicles and other combustibles) in EV fires are parallel to the flame central plane, whereas the flame area and the view factor parameters are related to the flame shape. The SFM was selected to simplify the flame shape analysis. It could better simulate the flame thermal radiation surface to study the range of influence of the thermal radiation of an EV thermal runaway fire. Compared to the PSM of the thermal radiation, this model was more accurate and, compared to the fire dynamics models of the thermal radiation, it was more simplified [17]. In this study, we made certain assumptions which are listed below:  
1. The flame of the EV fire was replaced by a hot surface with a stable geometry and constant emission power. 2. The emissivity of the flame-emitting surface of the SFM was wavelength-independent and radiated uniformly. 3. The flame in the vehicle combustion stage exited from the head and body of the vehicle. The view factor between the pedestrian and the flame surface was calculated using the flame radiation model and heat conservation. The pedestrians as the thermal radiation receptors can be regarded as many infinitesimal planes. To solve the view factors between the infinitesimal planes and the flame surfaces was a complex surface integral problem. So,the [PERSON] theorem was used to simplify the surface integral problem to a line integral along the boundary of the surface [19; 39]. The view factors of the vertical flame surface without airflow and a tilted flame surface with airflow (with a flame surface # 1--pedestrian and flame surface # 2--pedestrian) are presented below. (i)   Flame surface # 1--Pedestrian view factor is given by  
\[F_{\#1}=\frac{1}{2\pi}\left[