## 3 Results and Discussion  
### Model Validation  
Comparisons between \(T_{i1}\) (temperature of the driver's zone) and \(T_{i2}\) (temperature of passengers' zone) from the model simulation and from the actual coach cabin for the experiments in Table 4 are shown in Figures 5-7, respectively, where the setpoints are also  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Experiment** & \begin{tabular}{c} **Initial Cabin** \\ **Temetures** \\ **(\(T_{i1,0}/T_{i2,0}\))** \\ \end{tabular} & \begin{tabular}{c} **Outside** \\ **Temperature** \\ **(\({}^{\circ}\)C)** \\ \end{tabular} & \begin{tabular}{c} **Solar Irradiance** \\ **(W/m\({}^{2}\))** \\ \end{tabular} & \begin{tabular}{c} **Experiment** \\ **Time of Day** \\ \end{tabular} & \
\begin{tabular}{c} **Weather** \\ **Conditions** \\ \end{tabular} &
\begin{tabular}{c} **Number of** \\ **Passengers** \\ \end{tabular} \\ \hline
1 & 5.2 / 5.7 & 0–10 & 0 & Night & Foggy & 5 \\
2 & 13.8 / 17.1 & 7–16 & \(\approx\)200 & Noon & Sunny & 4 \\
3 & 18.2 / 19.4 & 16.5–19 & \(\approx\)200 & Afternoon & Sunny & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Operating conditions of selected validation tests.  
shown. Such simulations were performed using the Simulink environment from MATLAB version R2022a (Mathworks, Natick, MA, USA), where the model was implemented with a masked subsystem shown in Figure 8a and the solver used was an explicit fixed-step fourth-order Runge-Kutta. The unmasked model is also shown in Figure 8b for a better description of its implementation.  
Figure 5: Comparison between \(T_{i1}\) and \(T_{i2}\) from model simulation and actual experimental coach data (Experiment 1).  
Figure 6: Comparison between \(T_{i1}\) and \(T_{i2}\) from model simulation and actual experimental coach data (Experiment 2).  
Inputs \(T\_H1\) and \(V\_H1\) in Figure 8a are the temperature of the air and the supplied air flow rate from the heating system of the driver's zone, respectively. Likewise, inputs \(T\_H2\) and \(V\_H2\) are associated with the heating system of the passengers' zone. Lastly, input \(T\_o\) is the outside temperature and input \(I\) is the irradiance data. On the other hand,  
Figure 8: Simulink subsystem used for the coach cabin model. (**a**) Simulink mask. (**b**) Simulink unmasked model.  
Figure 7: Comparison between \(T_{i1}\) and \(T_{i2}\) from model simulation and actual experimental coach data (Experiment 3).  
outputs \(T\_i1\) and \(T\_i2\) are the simulated indoor mean temperatures of both thermal zones, respectively.  
Heat transfer coefficients and absorptivity were tuned using least-squares estimation from the experimental data, obtaining \(U_{inv}\approx 8\) W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\), \(U_{ow}\approx 3\) W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-1}\) and \(\alpha_{w}=0.19\).  
As can be seen from Figures 5-7, there is a close similarity between the model simulation and the experimental data for both transient behaviour and the steady state in the driver and passenger zones; minimal differences can be observed only at certain time intervals or instants for all experiments, often due to certain operational changes that cannot be accounted for in the model simulation; for example, variations in the engine temperature due to changes in vehicle speed. The maximum errors and the mean absolute errors (MAEs) between the experimental and simulated temperatures for each experiment are shown in Table 5 to quantify their similarity, which is also graphically shown in Figure 9. In experiments 2 and 3, the MAEs are close to zero and the maximum errors are approximately 1 \({}^{\circ}\)C, so they are not very significant. In experiment 1, however, the discrepancies are greater, but the MAEs still remain below 1 \({}^{\circ}\)C. This might be due to the irradiance parameter, which was not considered a tuning parameter in this experiment