## 3 Heat Load Estimation for an Electric Bus
### Heat Loss Due to the Doors Opening  
Estimating the heat loss through the open doors of the bus when it is stopped in stations is quite difficult, due to the air flow complexity between the inside of the bus and the exterior air of the environment, which depends on the random process of the weather conditions and wind speed and direction. The air is assumed to be an ideal gas and is compressible.  
When a pressure is applied to the interior air, the volume of the air is modified with a volume equal to the amount of the outside air, which is pressurized into the vehicle cabin, and therefore an air exchange is caused in the process. Some of the income air from outside is mixed with the inside air and is removed through the opening of the doors, due to the airflow direction change and due to the gradient of the temperature and the pressure, this is proportional to the surface area of the opening [33].  
The worst-case scenario is when the wind blows directly into the open door, as presented into the cross-section of the bus structure, showing an opened door (Figure 6).  
The heat loss through an open door of the bus is estimated with the following formula:  
\[\dot{Q}_{door}=\dot{V}\cdot\rho_{air}\cdot c\cdot\Delta T\;[\mathrm{W}], \tag{18}\]  
where \(\dot{V}\) is the flow rate of the air [m\({}^{3}\)/s], \(\rho_{air}\) is the air density 1.27 kg/m\({}^{3}\), and \(c\) is specific heat of the air 1009 J/kg\(\cdot\)K.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Thickness [m]** & **Thermal Conductivity [W/mK]** \\ \hline Iron & 0.002 & 76.2 \\ Laminated wood & 0.02 & 0.107 \\ Polyvinyl/PVC & 0.003 & 0.19 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The thicknesses and thermal conductivities for the materials of the floor of the bus.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**v [km/h]**} & \multicolumn{5}{c}{**U Value [W/m\({}^{2}\) K]**} & \multicolumn{5}{c}{\(\dot{Q}\)**Structure [W]**} & \multirow{2}{*}{\(\dot{Q}\)_amb_ [W]**} \\ \cline{2-3} \cline{5-10}  & **Uw** & **Uwall** & **Uroof** & **Ufloor** & \(\dot{Q}\)_w_ & \(\dot{Q}\)_wall_ & \(\dot{Q}\)_Proof_ & \(\dot{Q}\)_floor_ & \(\dot{Q}\)_amb_ [W]** \\ \hline
0 & 4.4 & 1.957 & 1.67 & 2.272 & 3832 & 1585 & 1458 & 2004 & 8879 \\ \hline
20 & 5.988 & 2.218 & 1.828 & 2.66 & 5209 & 1797 & 1595 & 2346 & 10,947 \\ \hline
40 & 6.45 & 2.283 & 1.87 & 2.747 & 5612 & 1849 & 1632 & 2425 & 11,518 \\ \hline
60 & 6.757 & 2.32 & 1.89 & 2.8 & 5878 & 1879 & 1653 & 2470 & 11,880 \\ \hline \hline \end{tabular}
\end{table}
Table 5: U values and heat loss through the bus structure into the ambient.  
According to [33], for a single opening enclosure (one open door), for a wind velocity of 10 m/s (a medium wind speed value during a cold day in winter), a flow rate of \(\dot{V}\) = 0.4 m\({}^{3}\)/s for a surface area of 1.44 m\({}^{2}\) is found. Thus, using Formula (17), heat losses result of \(\dot{Q}_{door}\) = 15,377 W for a single open door and, respectively, of \(\dot{Q}_{3 door}\) = 46,131 W for all the three open doors of the bus,  
Obviously, usually the doors do not stay open too frequently. The average stop time for a city bus is about 30 s [21], with an average running time between stops of 4 min, resulting the doors being open for 1/9 h. As consequence, the hourly heat loss from the open doors is 5.125 kW. Depending on the route, the number of stops, and the number of passengers getting on and off the vehicle, this heat loss may have various values.