## 2 Materials and Methods
### Governing Equations and Model Parameters
\[-\mathbf{n}\cdot\mathbf{q}=\varepsilon_{\mathrm{u}}\big{(}G_{\mathrm{u}}-n^{2} \sigma T_{0}^{4}\big{)}+\varepsilon_{\mathrm{d}}\big{(}G_{\mathrm{d}}-n^{2} \sigma T_{0}^{4}\big{)}, \tag{5}\]  
\[(1-\varepsilon_{\mathrm{u}})G_{\mathrm{u}}=j_{\mathrm{u}}-\varepsilon_{ \mathrm{u}}n^{2}\sigma T_{0}^{4}, \tag{6}\]  
\[(1-\varepsilon_{\mathrm{d}})G_{\mathrm{d}}=j_{\mathrm{d}}-\varepsilon_{ \mathrm{d}}n^{2}\sigma T_{0}^{4}, \tag{7}\]  
\[G_{\mathrm{u}}=G_{\mathrm{m,u}}(j)+F_{\mathrm{amb,u}}n^{2}\sigma T_{\mathrm{ amb,u}}^{4}+G_{\mathrm{extDir,u}}+G_{\mathrm{extDiff}} \tag{8}\]  
\[G_{\mathrm{d}}=G_{\mathrm{m,d}}(j)+F_{\mathrm{amb,d}}n^{2}\sigma T_{\mathrm{ amb,d}}^{4}+G_{\mathrm{extDir,d}}+G_{\mathrm{extDiff}} \tag{9}\]  
\[\mathbf{q}=-k\
abla T, \tag{2}\]0  
\[\mathbf{q}=-k\
abla T, \tag{2}\]1  
where \(T_{0}\) is the external temperature (K), \(\mathbf{n}\) is the normal vector (-), \(\varepsilon_{\mathrm{u}},\ \varepsilon_{\mathrm{d}}\) represent the upside and downside for the surface emissivity for acrylic plastic, \(\varepsilon_{\mathrm{u}}\ =\ \varepsilon_{\mathrm{d}}\ =\ 0.15\), \(\varepsilon\) is the surface emissivity for aluminum (covered with red paint), \(\varepsilon=0.96\), \(n^{2}\sigma T^{4}\) corresponds to blackbody emissive power according to Stefan-Boltzmann law (W/m\({}^{2}\)), \(n\) is the refractive index for the media (1), \(\sigma\) is the Stefan-Boltzmann constant (W/m\({}^{2}\)\(\cdot\)K\({}^{4}\)), \(j\) is surface radiosity (W/m\({}^{2}\)), \(j_{\mathrm{u}}\), \(j_{\mathrm{d}}\) is surface radiosity upside and downside, \(F_{\mathrm{amb}}\) is ambient view factor, in which \(F_{\mathrm{amb,u}}\), \(F_{\mathrm{amb,d}}\) are respectively the upside and downside, \(G_{\mathrm{m}}\) is mutual surface irradiation (W/m\({}^{2}\)), in which \(G_{\mathrm{m,u}}\) and \(G_{\mathrm{m,d}}\) are respectively the upside and downside, \(G_{\mathrm{extDir}}\) represents the directional external irradiation sources (W/m\({}^{2}\)), in which \(G_{\mathrm{extDir,u}}\), \(G_{\mathrm{extDir,d}}\) are respectively the upside, and downside, \(T_{\mathrm{amb}}\) is the ambient temperature (K), of which \(T_{\mathrm{amb,u}}\), \(T_{\mathrm{amb,d}}\) are respectively the upside and downside, \(G_{\mathrm{extDiff}}\) represesnts the diffuse external irradiation sources (W/m\({}^{2}\)). The assumed model parameters are summarized in \[\mathbf{q}=-k\
abla T, \tag{2}\]2 The other parameter values assumed in the numerical model are as follows: the heat source simulating the heat emitted due to the operation of LEDs was defined as the heat rate equal to \(Q_{LED}\) = 29 W/m\({}^{2}\), the heat source simulating the heat emitted due to the operation of stabilizers was defined as the heat rate equal to \(Q_{STAB}\) = 23 W/m\({}^{2}\), the ambient temperature \(T_{\mathrm{amb}}\) was varied in the range from 24 to 44 \({}^{\circ}\)C, but for the verification process \(T_{\mathrm{amb}}\) = 28 \({}^{\circ}\)C, the x-axis velocity component \(v_{x}\) of the velocity vector \(\mathbf{u}\) was varied in the range from 0 to 10 m/s, while the other components were assumed zero, except for the verification process \(v_{x}\) = 0 m/s. The inner part of the lamp and the tunnel was filled with air.