## 3 Results
### All Samples
So, similarly to what has been found by [35, 45], it can be seen in Figure 12 that the inclusion of PCM leads to a decrease of the thermal conductivity. Furthermore, a value of \(0.4\,\mathrm{W}\,\mathrm{K}^{-1}\,\mathrm{m}^{-1}\) has been estimated in the \(14.5\%_{w}\) case by [35], which is pretty close to the corresponding present cases (\(12.4\%_{w}\) and \(19.2\%_{w}\)) with \(\lambda_{s}=0.602\pm 3.74\%\,\mathrm{W}\,\mathrm{K}^{-1}\,\mathrm{m}^{-1}\) and \(\lambda_{l}=0.592\pm 2.86\%\,\mathrm{W}\,\mathrm{K}^{-1}\,\mathrm{m}^{-1}\), and \(\lambda_{s}=0.43\pm 2.03\%\,\mathrm{W}\,\mathrm{K}^{-1}\,\mathrm{m}^{-1}\) and \(\lambda_{l}=0.441\pm 3.54\%\,\mathrm{W}\,\mathrm{K}^{-1}\,\mathrm{m}^{-1}\). In the same way, [45] obtained values of \(0.49-0.5\,\mathrm{W}\,\mathrm{K}^{-1}\,\mathrm{m}^{-1}\) and \(0.42-0.48\,\mathrm{W}\,\mathrm{K}^{-1}\,\mathrm{m}^{-1}\) with \(10\%_{w}\) and \(20\%_{w}\), while the current \(12.4\%_{w}\) and \(22.1\%_{w}\) cases lead to \(\lambda_{s}=0.602\pm 3.74\%\,\mathrm{W}\,\mathrm{K}^{-1}\,\mathrm{m}^{-1}\) and \(0.383\pm 0.58\%\,\mathrm{W}\,\mathrm{K}^{-1}\,\mathrm{m}^{-1}\), and to \(\lambda_{l}=0.592\pm 2.86\%\,\mathrm{W}\,\mathrm{K}^{-1}\,\mathrm{m}^{-1}\) and \(0.386\pm 1.74\%\,\mathrm{W}\,\mathrm{K}^{-1}\,\mathrm{m}^{-1}\), respectively. In the same idea, the identified specific heat capacities are depicted in Figure 13. Due to the large discrepancies between all the data, no quantitative comparison can be done yet the results agree qualitatively, nevertheless, we can note that the present values are very close to each other. Lastly, by dividing the current latent heats obtained for each mortar, in Table 3, by the mass fraction of the PCM, one can express the latent heat in function of the specific mass of the PCM instead of the one of the mixture (cement+PCM). More clearly, this means that the latent heat of the PCM can be directly calculated and, then, compared to the experimental value of \(99\,\mathrm{k}\,\mathrm{k}\,\mathrm{k}^{-1}\), which was determined by DSC [68]. This measurement had been down with a Pyris Diamond apparatus from Perkin Elmer, using a \(5.78\,\mathrm{m}\mathrm{g}\) sample and a \(5\,\mathrm{K}\,\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{e} \mathrm{t}\) heating rate on dynamic mode. The corresponding results are shown in Table 5: once again, the agreement with the experimental measure is very good, a standard deviation of \(3.56\%\) being observed for a mean value of \(95.47\,\mathrm{k}\,\mathrm{k}\,\mathrm{k}^{-1}\). The associated discrepancy with the experimental measurement is of \(1.23\%\), which is excellent given all the experimental and numerical uncertainties. Figure 10: Comparisons of the identified enthalpy functions for all the mortars (_n.b._ unique formulation pertaining for both fusion and crystallization). Figure 11: Comparisons of the enthalpy functions obtained with minimal (blue) and maximal (red) values of the identified parameters, together with the absolute discrepancy, for all the mortars (_n.b._ unique formulation pertaining for both fusion and crystallization). \begin{table}
\begin{tabular}{c c c c} \hline  & **12.4\%\({}_{uv}\)** & **19.2\%\({}_{uv}\)** & **22.1\%\({}_{uv}\)** \\ \hline Avg. (J kg\({}^{-1}\)) & 99,696 & 94,930 & 94,792 \\ \(\epsilon\) & 0.7\% & 4.11\% & 4.25\% \\ \hline \end{tabular}
\end{table} 
Table 5: Estimated values of the micronal latent heat and comparison with the experimental value obtained by DSC [68]. Eventually, another aspect of the inversion procedure is going to be analyzed by considering the identified values for the thermal parameters, that is to say the thermal conductivities and the thermal resistances furnished in Table 3. One can see that the former ones are pretty well estimated, the discrepancy being several orders below the usual uncertainties for PCM measurements. In contrast, the determination of the thermal resistances is more tricky, which is very well known.