## 3 Heat Load Estimation for an Electric Bus
### Solar Heat Loads
#### 3.2.4 Solar Heat Gain Estimation for Romania
Heat Flow Due to the Fresh Air Supplied by Ventilation, Which Is Necessary for Passengers' Needs--\(\dot{Q}_{oxn}\)  
Ventilation and ambient loads are functions of the temperature difference between the cabin and the ambient load. The air flow rate for the buses depends on the operating of the air conditioning system, with values between the 0.05 m\({}^{3}\)/s and 0.3 m\({}^{3}\)/s [28]. For the city buses with frequently stops, the fresh air supplied by ventilation is dominated by the air flow through the open doors, and the ventilation can be used for the lower value, which is 0.05 m\({}^{3}\)/s [28]. Heat transfer due to the ventilation can be estimated with Formula (8) and depends on the temperature difference (\(\Delta T\)), the specific heat, the air density (\(\rho_{air}\)) and the air flow rate (\(\dot{V}\)) [29], as follows:  
\[\dot{Q}_{oxn}=\dot{V}\cdot\rho_{air}\cdot\cdot\cdot\Delta T\ \ \ [\text{W}], \tag{8}\]  
For an air flow rate of 0.05 m\({}^{3}\)/s, an air density of 1.27 kg/m\({}^{3}\), a specific heat of 1009 J/kg\({}^{4}\)K, and a gradient of temperature of 30 \({}^{\circ}\)C, the heat transfer due to the ventilation is \(\dot{Q}_{oxn}\) = 1.922 kW. Heat Flow Changes with the Ambient Load Due to the Temperature Gradient between the Bus Structure and the Exterior Environment (Ambient Heat Load)--\(\dot{Q}_{amb}\)  
Heat transfer takes place from warm bodies (areas) to colder bodies (areas). So, in the winter cold days, the heat transfer takes place from the heated bus cab to the cold outside environment Thus, a large amount of heat is loss into the atmosphere through the windows, walls, roof, floor, and doors. This heat loss depends on the area of the surfaces, on the heat transfer coefficient (for each material or an overall estimated coefficient), and on the inside and outside temperatures. The heat transfer is estimated considering the conduction through solid materials, the convection between the interior air in the bus and \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(HA_{12}\) & \begin{tabular}{c} **Average Solar Irradiation,** \\ **[W/m\({}^{2}\)]** \\ \end{tabular} & \begin{tabular}{c} **Bus Windows** \\ **Area, [m\({}^{2}\)]** \\ \end{tabular} & \(\tau\) & \
\begin{tabular}{c} **Average Heat** \\ **Gain [kW]** \\ \end{tabular} &
\begin{tabular}{c} **Daily Average Heat** \\ **Input, [W/m\({}^{2}\)]** \\ \end{tabular} \\ \hline \hline December & 0.36 & 63.24 & & & 1.38 & 8.25 \\ \hline January & 0.39 & 126.99 & 29 & 0.75 & 2.76 & 16.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average heat gain for both direct and diffused solar radiation. the inner surfaces, and the convection between the exterior air and the outer surfaces of the bus (Figure 2). For a wall composed by a single layer, the heat transfer is calculated with the following equation:  
\[\dot{Q}=A\cdot U\cdot(T_{i}-T_{o})\ \ \ [W], \tag{9}\]  
where \(A\) is the cross-sectional area [m\({}^{2}\)], \(U\) is the heat transfer coefficient [W/m\({}^{2}\) K], \(T_{i}\) is the inside temperature [\({}^{\circ}\)C], and \(T_{o}\) is the outside temperature [\({}^{\circ}\)C],  
The heat transfer coefficient is calculated as a combination of conductive and convective heat transfer, which is given by [18]:  
\[\frac{1}{U}=\frac{1}{h_{i}}+\frac{L}{k}+\frac{1}{h_{o}}, \tag{10}\]  
where \(h_{i}\) is convective heat transfer coefficient between the interior air and the inner surfaces of the wall [W/m\({}^{2}\) K], \(h_{o}\) is the convective heat transfer coefficient between the exterior air and the outer surfaces of the wall [W/m\({}^{2}\) K], L is the thickness of the wall [m], and \(k\) is the conductive heat transfer coefficient of the wall [W/mK]. For the vehicles, the convection coefficients of the outer surfaces depend on the vehicle speed, and for the inner space, the coefficient depends on the air speed inside, relative to the inner surfaces [18], as follows:  
\[h=9+3.5v^{0.66}\ \ \ [W/m^{2}\text{ K}], \tag{11}\]  
with \(v\) as the relative air speed to the surface [m/s].