## 3 Numerical Calculation Method of Automobile Dynamic Heat Transfer Model
### Dynamic Radiation Heat Transfer Inside and Outside the Car  
The radiation on the exterior surface of the car mainly includes direct solar radiation, diffuse solar radiation, ground radiation, sky radiation and the radiation from the exterior car body to the external environment. Therefore, the net radiative heat rate of node element \(i\) on the exterior surface \(Q_{\text{rad},i}\) can be written as  
\[Q_{\text{rad},i}=A_{i}\alpha_{i}(I_{\text{D}}\cos\theta_{i}+I_{\text{d}})+A_{i }\alpha_{i}\sigma(F_{\text{g},i}T_{\text{g}}^{4}+F_{\text{s},i}T_{\text{s}}^{4 })-A_{i}\varepsilon_{i}E_{\text{b},i} \tag{2}\]  
\(A\), \(\alpha\) and \(\varepsilon\) represent the area, absorptivity and emissivity of the node element, respectively; \(I_{\text{D}}\) and \(I_{\text{d}}\) are the direct and scattered solar radiation intensity, respectively, which are measured and recorded by the experimental instrument in real time; \(\theta\) is the solar incident angle; \(E_{\text{b}}\) is the blackbody radiation force, \(E_{\text{b}}=\delta T^{4}\); \(\sigma\) represents the Stefan-Boltzmann constant, \(5.67\times 10^{-8}\) W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-4}\); and \(T_{\text{g}}\) and \(T_{\text{s}}\) represent ground environmental temperature and sky effective temperature respectively, which is given by Swinbank as the Formula (3) [32]. \(T_{\text{ex}}\) is the air temperature at an altitude of about 1.5 m from the ground outside the vehicle, which was measured in real time by a small climate station. \(F_{\text{g},i}\) and \(F_{\text{s},i}\) represent the angular coefficients of the ground environment and the sky to node \(i\) respectively, which can be calculated by Formulas (4) and (5) [32; 33; 34]. \(\psi\) is the angle between the node element and the horizontal plane. \[T_{\text{s}}=0.0552T_{\text{ex}}^{1.5} \tag{3}\]  
\[F_{\text{g},i}=(1-\cos\psi_{i})/2 \tag{4}\]  
\[F_{\text{s},i}=(1+\cos\psi_{i})/2 \tag{5}\]  
The window glass exhibits highly selective transmittances to the radiation of different wavelengths, in which the solar short-wave radiation can pass through the window glass and enters the cabin with a certain transmittance [35]; however, the transmittance of the window glass to the long-wave radiation is very low [36; 37; 38]. Therefore, it can be considered that the long-wave radiation in the cabin can't pass through the window glass [39; 40]. The incident solar radiation in the cabin mainly consists of direct solar radiation that reaches node element \(i\) in the cabin through the window glass, diffuse solar radiation and solar radiation that falls on node element \(i\) after being reflected by other element \(j\) in the cabin. According to the interchangeability of the angle coefficients, the solar radiation heat rate absorbed by element \(i\) in the cabin \(Q_{\text{s},i}\) and the incident solar radiation intensity \(I_{\text{s},i}\) on element \(i\) can be, respectively, represented as  
\[Q_{\text{s},i}=A_{i}\alpha_{i}\sum_{j=1}^{u}\left(f_{ij}\tau_{j}I_{\text{D}} \cos\theta_{j}+F_{ij}\tau_{j}I_{\text{d}}+F_{ij}\rho_{j}I_{\text{s},j}\right) \tag{6}\]  
\[I_{\text{s},i}=\sum_{j=1}^{u}\left(f_{ij}\tau_{j}I_{\text{D}}\cos\theta_{j}+F_ {ij}\tau_{j}I_{\text{d}}+F_{ij}\rho_{j}I_{\text{s},j}\right) \tag{7}\]  
\(u\) represents the number of nodes on the interior trims; \(\tau\) and \(\rho\) are the transmittance and reflectivity, respectively; \(f_{ij}\) is the area projection factor of element \(i\) on element \(j\)[41]; and \(F_{ij}\) is the angle coefficient of element \(i\) to element \(j\). There are phenomena of multiple reflection and absorption of long wave radiation emitted by the elements in the cabin, which enhances the calculation complexity of radiative heat transfer in the cabin. However, by means of calculating the surface effective radiation and net radiation, the complex radiant energy transfer process in cabin can be analyzed concisely and intuitively.