## 8 Results
### Single Roof  
As mentioned above, the roofs' thermal behavior was analyzed using the weather data of the week with the warmest outdoor air temperatures of 2018 using weather data from four representative towns in Mexico with a warm climate. The detailed results of Hermosillo are shown here because it was the town with the highest outdoor temperature. At the end of this subsection, a summary table presents the results of the thermal evaluation of the single roof in all cities. For Hermosillo Sonora, the days selected were from 30 May to 5 June 2018 because this was the week with the highest temperatures of the year. Figure 4a shows the solar irradiation and the wind speed during the seven days analyzed. The maximum solar radiation was around 1000 W/m\({}^{2}\). According to the behavior of solar irradiance, all days selected were clear days without clouds. The maximum wind speed reached around 5 m/s. Figure 4b shows the air temperature; due to the type of weather of this city, the ambient air reached very high temperatures, with an average maximum temperature of 45 \({}^{\circ}\)C.  
Figure 4b presents the temperature of the exterior surface of the roofs and the ambient air temperature during the selected week. Conventional roofs had a similar behavior, and on the other hand, reflective roofs maintained a similar behavior concerning the temperature of the exterior surface. This effect occurred because the solar reflectance of conventional coatings was very similar. The exterior surface of the roofs reached its maximum temperature between 14:30 and 15:00 h. The exterior surface of the single terracotta roof (STR), the single gray roof (SGR), Single White Roof #1 (SWR1), and Single White Roof #2 (SWR2) reached on average 61, 59, 45, and 43 \({}^{\circ}\)C, respectively. These values indicated that applying the terracotta coating, on average, increased the temperature of the exterior surface by 2 \({}^{\circ}\)C compared to the SGR. In contrast, SWR1 and SWR2 reduced the temperature of the exterior surface by on average 14 and 16 \({}^{\circ}\)C, respectively. Furthermore, if the average maximum temperatures of reflective roofs were compared with the average maximum temperature of ambient air (45 \({}^{\circ}\)C), SWR1 had the same maximum temperature as the ambient air. In contrast, SWR2 reached a temperature of 2 \({}^{\circ}\)C lower than the maximum air temperature. On the other hand, the SGR and STR reached a temperature of 14 and 16 \({}^{\circ}\)C higher than the ambient air temperature. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Coating** & **Solar Absorptance (\(\alpha\))** & **Thermal Emittance (\(\varepsilon\))** \\ \hline Gray & 0.67 & 0.87 \\ Terracotta & 0.70 & 0.88 \\ White \# 1 & 0.20 & 0.90 \\ White \# 2 & 0.16 & 0.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optical properties of the coatings. Figure 4c presents the temperature of the single roofs' interior surface. The interior surface of the roofs reached their maximum temperature between 16:00 and 16:40 h. The temperature of the interior surface of the STR, SGR, SWR1, and SWR2 reached a maximum temperature of 51, 49, 38, and 37 \({}^{\circ}\)C, respectively. Therefore, the influence of a reflective coating on the interior surface temperature was obtained by comparing the previous temperature values. SWR1 decreased the temperature of the interior surface by around 10 \({}^{\circ}\)C compared to the SGR, while SWR2 reduced the temperature of this surface by around 11 \({}^{\circ}\)C.  
Figure 4d shows the behavior of the heat flux of the roofs in Hermosillo during the seven days analyzed. The maximum heat flux traveling through the roofs occurred between 16:00 and 16:50 h. The STR, SGR, SWR1, and SWR2 had an average peak heat flux of 157, 150, 87, and 82 W/m\({}^{2}\), respectively. These values indicated that the peak heat flux crossing SWR1 and SWR2 was 41% and 45% smaller than that corresponding to the SGR, while the heat flux of the STR was 5% greater than that of the SGR.