## 4 Results
### Time Lag and Diffusivity  
The analysis consisted of calculating the diffusivity and lag values of the different materials used to build the proposed roofs. Table 12 shows the thermal diffusivity values of the materials and the time lag of the thermal characteristic of each of them.  
In the case of the materials that constitute the proposed roofs, the material with the highest diffusivity corresponds to the highest conductivity material, the reticular ironwork. In contrast, the material with the lowest diffusivity corresponds to the material whose specific heat product and density is higher, i.e., water. Its low diffusivity is due to the high value of the specific heat capacity. Materials with high diffusivity are observed to have low times lags, while low-diffusivity materials have high times lags.  
To achieve reductions in thermal amplitudes, enclosures must have low diffusivity. In the case of enclosures composed of several layers, the low-diffusivity materials must be located on the outer side of the enclosure. Table 13 details the time lag value at the construction section level of the roofs under study (see Figures 9 and 10).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Loff Flat Roofs. Housing Block**} & \multicolumn{2}{c}{**Exhibition Hall Roofs. MUA**} \\ \hline \multicolumn{2}{c}{**Decrement Factor, \%**} \\ \hline Sections & \multicolumn{2}{c}{Sections} & \\ Q\_R\_1 & 88.82\% & Q\_M\_1 & 92.14\% \\ Q\_R\_2 & 87.89\% & Q\_M\_2 & 89.66\% \\ Q\_R\_2\_1\_0.15 & 97.45\% & Q\_M\_2\_1\_0.15 & 97.77\% \\ \hline \hline \end{tabular}
\end{table}
Table 11: Decrement factor values of the roof sections under study.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Material** & **Diffusivity, m\({}^{2}\)/s** & **Time Lag, h** \\ \hline \multirow{3}{*}{04} & Thermal insulation: XPS & \multirow{3}{*}{\(8.53\times 10^{-7}\)} & \multirow{3}{*}{0.75} \\  & [0.032W/[mK]] & & \\ \cline{1-1}  & Membrane: Non-woven geotextile & & \\ \cline{1-1}  & Thermosol & & \\ \cline{1-1}
06,08 & Mortar bed & & \\ \cline{1-1}
09 & Aerated concrete & & \\ \cline{1-1}
13 & Water proofing membrane: & & \\ \cline{1-1}  & LBM-30-FV, LBM-40-FP & & \\ \cline{1-1}
16 & Paving file & & \\ \cline{1-1}
18 & Marble & & \\ \cline{1-1}
21 & Water & & \\ \cline{1-1}
22 & Trim and plaster & & \\ \cline{1-1}
23 & Plasterboard & & \\ \cline{1-1}
25 & Air gaps. No ventilated R = 0.28 & & \\ \cline{1-1}
27 & Reinforced concrete (reticular) & & \\ \cline{1-1}
42 & Reinforced concrete & & \\ \cline{1-1}
43 & GAlvanized steel sheet & & \\ \hline \hline \end{tabular}
\end{table}
Table 12: Thermal diffusivity and time lag of the materials composing the roof sections under study.  
The time lag values of the water-covered roofs are on average between 31% and 34% higher than the values obtained for roofs made of terrazzo paving and marble. The times lags of the Q\({}_{\text{R}}\_1\), 2 and Q\({}_{\text{M}}\_1\), 2 are very similar. This is because the roofs are very similar in terms of mass value. The difference between them lies in the relative position of thermal insulation, a material whose mass is negligible with respect to the enclosure as a whole.