## 4 Results and Discussion
### Test of the Numerical Model with Various Thermal Solicitations  
To verify the effectiveness of the model just built, the same sample was loaded in several different ways. Figures 14 and 15 show the results obtained for the case of temperature stress in the form of a 3-h and 6-h ramp. Figure 16 displays a comparison between the experimental fluxes and those obtained numerically, for the case of an asymmetric loading. Various temperatures were imposed on the left and right sides of the sample at different heat \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(T_{A\,=}\) & 29.02 & \(T_{A\,=}\) & 23.94 & \(\lambda_{S}\) = 0.135 & \(c_{S}\) = 1213 & L\({}_{A}\) = 126,300 \\ \hline \(T_{M_{m}}\) & 26.89 & \(T_{M_{s}}\) & 22.71 & \(\lambda_{L}\) = 0.128 & \(C_{L}\) = 1124 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Thermal characteristics of ETMV 8. Figure 13: Evolution of the flux exchanged between the plate and the sample (10-h ramp). \begin{table}
\begin{tabular}{c c c} \hline \hline \((1-\psi_{\text{m}}).\text{L}_{A}\) & 81,942 & \(\text{a}_{\text{m}}\) = 24.18 & \(\text{b}_{\text{m}}\) = 0.98 \\ \hline \hline
**Parameters of the function \(\mathbf{f}_{\text{Gumbel}}\) solidification** & \\ \hline \((1-\psi_{\text{s}}).\text{L}_{A}\) & 12,300 & \(\text{a}_{\text{s}}\) = 17.74 & \(\text{b}_{\text{s}}\) = 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters of the Gumbel function. It was also necessary to test the model under constraints leading to partial state changes of the PCM. The problem arising with partial phase changes is mainly caused by the transition between the melting and solidification processes. In the literature, two methods are basically employed to model these types of PCM state changes. Several authors, including [PERSON] et al. [54], have suggested an absence of hysteresis until the PCM is completely melted or solidified. This assumption implies no difference between the state changes of the material as it alternates between melting and solidification. The approach proposed by [PERSON] et al. [54] thus maintains the same liquid fraction curve as a function of the PCM state (Figure 17a). When inducing changes in the partial melting states, only the liquid fraction curve is therefore used in the melting phase. On the other hand, when carrying out a partial solidification, only the liquid fraction curve in the solidification phase gets used, along the opposite direction of the curve when the temperature variation is reversed. Another method that takes PCM hysteresis into account also exists, leading [PERSON] et al. [55] and [PERSON] et al. [56] to propose alternating between the melting and solidification liquid fraction curves, depending on the temperature stresses imposed on the material (Figure 17b). [PERSON] et al. [54] compared the accuracy of these two methods and found relative similarity. Other authors, namely [57; 58], have come up with different opinions; they have shown, through studies on walls containing PCM, that the hysteresis of the PCM plays an important role and has a significant impact on both the energy balance and thermal performance of the material. The studies in [26; 58] compared the two methods and issued a divided opinion on the subject. They concluded that the efficiency of both methods depended on the PCM phase. Notably, [PERSON] et al. [26] observed that although the method taking PCM hysteresis into account is more accurate, it nonetheless does not allow for a satisfactory representation of the partial melting. The hybrid model proposed in this paper, incorporating supercooling, was developed with the first method, which does not take hysteresis into account when analyzing melting and partial solidification. Further studies will draw a comparison of these two methods.