## 4 Heat Transfer Equation and Thermal Boundary Conditions
\[\mathrm{I}_{\mathrm{s}}=\frac{\mathrm{cos}\ \theta}{\mathrm{cos}\ \beta}\mathrm{I}_{ \mathrm{dh}}+\frac{1+\mathrm{cos}\ \delta}{2}\ \mathrm{I}_{\mathrm{dh}}+\mathrm{I}_{ \mathrm{gr}} \tag{4}\]  
\[\mathrm{I}_{\mathrm{gr}}=\mathrm{r}_{\mathrm{g}}\ \left(\mathrm{I}_{ \mathrm{bh}}+\mathrm{I}_{\mathrm{dh}}\right)\ \frac{1-\mathrm{cos}\ \delta}{2} \tag{5}\]  
\[\mathrm{q}_{\mathrm{s}}=\alpha\ \mathrm{(I}_{\mathrm{s}}\ ) \tag{6}\]  
where I\({}_{\mathrm{bh}}\) and I\({}_{\mathrm{dh}}\) represent the beam and diffuse solar radiations striking the horizontal surfaces, respectively. The heat transfer convection \(\mathrm{(q}_{\mathrm{con}}\)) between the ambient air and the girder surfaces can be determined as expressed in Equation (7). This convection of heat is considered a cooling process and is determined by the difference between the surface temperature \(\mathrm{(T}_{\mathrm{s}}\ )\) and ambient air temperature \(\mathrm{(T}_{\mathrm{a}}\)). The surface convection coefficient of heat transfer \(\mathrm{(h}_{\mathrm{c}}\)) controls the rate of heat exchange, which is measured in W/m\({}^{2}\cdot\)k. \(\mathrm{(h}_{\mathrm{c}}\)) is a function of wind speed (u) as presented in Equation (8) [37]. \[\mathrm{q}_{\mathrm{con}}\ =\mathrm{h}_{\mathrm{c}}\mathrm{(T}_{\mathrm{s}}- \mathrm{T}_{\mathrm{a}}\ ) \tag{7}\]  
\[\mathrm{h}_{\mathrm{c}}\ =\ 4\mathrm{u}\ +\ 5.6\ \ \mathrm{(u}\ <\ 5\,\mathrm{m}/ \mathrm{s}) \tag{8}\]  
The longwave radiation \(\mathrm{(q}_{\mathrm{re}}\)) represents the heat emitted from the exposed surfaces to the surrounding atmosphere due to thermal irradiation. \(\mathrm{(q}_{\mathrm{re}}\)) depends on the surface emissivity of the girder (e), the Stefan-Boltzman constant (F) which is \(5.67\times 10^{-8}\) W/m\({}^{2}\) k4 and the difference between the surface temperature and ambient air temperatures presented in Equation (9). This longwave radiation \(\mathrm{(q}_{\mathrm{re}}\)) is of particular importance when assessingthe thermal performance of the girder, as it has the potential to significantly impact the temperature of the girder and its surrounding environment. \[\mathrm{q_{re}}\ =\ \mathrm{eF}\ \mathrm{\left(T_{s}^{4}-T_{a}^{4}\right)} \tag{9}\]  
The shaded length of the web can have a significant influence on the temperature of the web surface. The shaded length of the web (\(\mathrm{L_{S}}\)) varies with the sun's movement, and the shaded part of the web can be calculated as presented in Equation (10). The calculation of the shaded length depends on the length of the overhang (\(\mathrm{L_{C}}\)), the angle between the web and the horizontal direction (\(\mathrm{\beta}\)), the solar altitude angle (h) and the solar azimuth angle of the sun (\(\mathrm{\varphi}\)). The shaded parts of the web have a lower heat than those without shade. This is because the shaded parts are not exposed to the direct (beam) solar radiation component. Figure 2:0  
The study by [PERSON] and [PERSON] can be used to determine and calculate the solar incident angle, altitude angle, azimuth angle and other geometric factors [40; 41]. The thermal boundary conditions of heat fluxes (\(\mathrm{q}\)) that describe the thermal loads and the heat transfer equation that depends on the thermal material properties are numerically complicated to solve. Therefore, ANSYS finite element software is used to conduct thermal analysis.