## 8 Results
### Insulated Roof  
The insulated roof was studied also in Hermosillo as it was the warmest city among the selected locations. As in the previous section, first, the detailed analysis of this city is presented, and then, the results for other cities are summarized at the end of this subsection. Figure 5b shows the behavior of the temperature of the external surface of the insulated roofs and the temperature of the ambient air during the seven days considered. Insulated roofs with a conventional color had a similar behavior, and on the other hand, the insulated roofs with reflective coating maintained a similar behavior regarding the temperature of the exterior surface. The exterior surface of the roofs reached its maximum temperature between 13:30 and 14:00 h. The exterior surface of the insulated terracotta roof (ITR) reached on average 72 \({}^{\circ}\)C, the insulated gray roof (IGR) 69\({}^{\circ}\), Insulated White Roof #1 (IWR1) 50 \({}^{\circ}\)C, and Insulated White Roof #2 (IWR2) 49 \({}^{\circ}\)C. These temperatures indicated that ITR had on average a temperature of the exterior surface about 3 \({}^{\circ}\)C higher than the IGR, while IWR1 and IWR2 reduced the temperature of the exterior surface by 19 and 20 \({}^{\circ}\)C on average, respectively. If the average maximum temperatures of white reflective roofs were compared with the average maximum temperature of ambient air (45 \({}^{\circ}\)C), IWR1 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**City** & **Roof** & \(T_{es}\) (\({}^{\circ}\)C) & \(T_{is}\) (\({}^{\circ}\)C) & \(Q_{R}\) (\(\frac{\text{W}}{\text{m}^{2}}\)) & \(HG\) (\(\frac{\text{W}}{\text{m}^{2}-\text{day}}\)) \\ \hline \multirow{4}{*}{Monterrey} & SGR & 51 & 43 & 113 & 1109 \\  & SWR1 & 38 & 34 & 56 (\(-\)50\%) & 563 (\(-\)49\%) \\  & SWR2 & 37 & 33 & 52 (\(-\)54\%) & 520 (\(-\)53\%) \\  & STR & 53 & 45 & 121 (\(+\)7\%) & 1213 (\(+\)9\%) \\ \hline \multirow{4}{*}{Hermosillo} & SGR & 59 & 49 & 150 & 1675 \\  & SWR1 & 45 & 39 & 87 (\(-\)42\%) & 1045 (\(-\)38\%) \\  & SWR2 & 43 & 38 & 82 (\(-\)45\%) & 993 (\(-\)41\%) \\  & STR & 61 & 51 & 157 (\(+\)5\%) & 1793 (\(+\)7\%) \\ \hline \multirow{4}{*}{Villahermosa} & SGR & 50 & 43 & 111 & 1097 \\  & SWR1 & 37 & 34 & 53 (\(-\)52\%) & 550 (\(-\)50\%) \\ \cline{1-1}  & SWR2 & 36 & 33 & 48 (\(-\)57\%) & 506 (\(-\)54\%) \\ \cline{1-1}  & STR & 52 & 44 & 120 (\(+\)8\%) & 1219 (\(+\)11\%) \\ \hline \multirow{4}{*}{Mérida} & SGR & 53 & 43 & 123 & 1148 \\ \cline{1-1}  & SWR1 & 39 & 34 & 61 (\(-\)50\%) & 569 (\(-\)50\%) \\ \cline{1-1}  & SWR2 & 38 & 33 & 56 (\(-\)54\%) & 511 (\(-\)54\%) \\ \cline{1-1}  & STR & 55 & 44 & 131 (\(+\)7\%) & 1255 (\(+\)9\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the thermal evaluation of a single roof in four cities of Mexico (Average peak values for the different variables). had a maximum temperature of 5 \({}^{\circ}\)C above the maximum air temperature, while the IWR2 roof reached a temperature 4 \({}^{\circ}\)C higher than the maximum air temperature. On the other hand, the IGR and ITR reached a temperature of 23 and 26 \({}^{\circ}\)C higher than the maximum ambient air temperature, respectively. Figure 5c shows the temperature of the interior surface of the four roofs. Due to thermal insulation, the temperatures of the roofs' interior surface had a small oscillation between day and night compared to the cases without insulation. These surfaces reached their maximum temperature between 17:30 and 18:10 h. The temperature of the interior surface of the ITR and that of the IGR reached a maximum temperature of 29.3 \({}^{\circ}\)C and 29 \({}^{\circ}\)C, while the surface temperature of IWR1 and IWR2 reached 27.4 \({}^{\circ}\)C and 27.2 \({}^{\circ}\)C. This figure demonstrates that the insulation caused the interior temperature of the roofs to remain relatively constant. Figure 5d shows the behavior of the heat flux of the insulated roofs in Hermosillo.