## 4 Results and Discussion  
### Optimization of the Numerical Model Parameters  
The experimental set-up described above (Figure 4) has been used to characterize the ETMV 8 coating. The sample was stressed by temperature ramps ranging from 3 h to 10 h. The fluxes measured for each case are shown in Figure 12; it can be observed that the measured flux has a shape that varies greatly with the duration of the adopted temperature ramp. Similar behavior has already been observed and detailed by [PERSON] et al. [21]. The melting of the PCM is progressive during the heating ramps, the material stores sensible and latent heat. The maximum flux density is reached at the end of the temperature ramp and then returns to a zero value until the material returns to an isothermal thermal state. Let us notice in particular that the use of a temperature ramp of short duration during cooling, e.g., 3 h, does not expose the second flux peak, which is caused by the presence of several materials in the PCM. This second peak is only visible from the 5-h temperature ramp because for the faster ramp (3-h), the temperatures vary too quickly, and the two energy release peaks occur at very close times. However, when installed in a building, the material rises in temperature over periods that can be on the order of one day. It is therefore important to take these longer periods into account.  
It is therefore essential to use a large temperature ramp to more accurately determine the thermal characteristics of the coating. In this study, the thermal characterization of the sample was performed with the experimental measurements of the test performed with the T-10H thermal loading ramp.  
From these heat flux and temperature measurements, inverse methods allow for determining: thermal conductivity, heat capacity in the solid and liquid states, thermal contact resistances between the plates and the sample, and latent heat. This latent heat (126 kJ/kg) is most consistent since it closely corresponds to 70% of the latent heat of PCM (180 kJ/kg), as obtained by the DSC method [52; 53]. The melting temperatures TA (melting temperature of the pure solvent) and TM (temperature of the liquidus) are also evaluated. The resulting parameters are as follows (Tables 4 and 5):  
Figure 12: Evolution of the heat flux (F–xH) exchanged between the plate and the sample, for various temperature ramps (T–xH): melting phase (**a**), and solidification phase (**b**).  
These parameters serve to numerically simulate the thermal behavior of the coating. Figure 13 shows a comparison between the thermal flux measured experimentally and that calculated with the numerical model and optimized parameters. This figure reveals that the model presented herein, i.e., the derivative of enthalpy coupled with a Gumbel function, yields strong results (as opposed to the model of a simple binary solution) and moreover accurately reproduces the behavior of the ETMV 8 coating, whether during melting or solidification; in particular, it allows reproducing the effect of supercooling during the solidification phase.  
It has been demonstrated that the dynamics of the melting and solidification processes are well represented by the numerical model developed above. It remains to be verified that this model is efficient for various loadings and in the case of partial melting or solidification since these cases are difficult to model and can lead to errors in the calculation of energy balances.