## 1 Introduction
In addition, the heating rate affects DSC results and can induce errors in the determination of thermal properties [20]. Non-DSC methods rely on enthalpy evolution to study the thermodynamic behavior of PCMs. According to [PERSON]. [PERSON] et al. [21], most of these other methods, which generally consider the PCM as a binary solution, have limitations and do not always correctly represent the PCM thermal behavior. Moreover, the fatty acid mixture studied here is not a binary solution. Indeed, the two components of Inertek 23, i.e., methyl palmitate and methyl stearate, display completely different thermal properties (Figure 1b). Let's also note that the transitions between solid/liquid phases during the state changes of the two materials do not occur over the same temperature range. The supercooling phenomena that may occur in mixtures are difficult to analyze with the classical methods reported in the literature. Supercooling reflects the ability of the PCM to lower its temperature below the crystallization point while remaining in liquid form. This supercooling effect can be a drawback if the degree of supercooling is too high by virtue of preventing energy discharge of the PCM [22]. Under these conditions, the stored heat is released at a temperature below the PCM melting temperature. This article presents the thermophysical characterization of a coating (ETMV 8) sample tested in the laboratory. The sample's properties are determined through experimental measurements (conducted in LGCgE laboratory on a fluxmeter bench) combined with identification techniques using inverse methods, by relying on a new numerical model. This numerical model is necessary to reliably represent the thermal behavior of the coating during solid/liquid phase transitions. This numerical model is also intended to integrate a thermal simulation software at the building scale. The thermophysical characterization is performed during the melting and solidification phases of the PCM. The particularities of this PCM are that it is encapsulated and issued from a mixture of two PCM. This produces a specific thermal behavior of the material which is little dealt with in the literature. The melting of the PCM mixture shows a progressive melting of the two PCM in a simultaneous way. On the other hand, on cooling the material exposes the phenomenon of supercooling and shows a dissociated solidification of the two mixed PCM. To establish the numerical model of the composite material (gypsum + microencapsulated PCM), temperature ramps of varying lengths were imposed on the material, corresponding to the thermal dynamics observed in buildings, which is the aimed application for this material. The very different heating and cooling behavior of the PCM associated with the supercooling phenomenon is an issue for the choice of the analytical model. Many researchers [23] consider the assumption of a hysteresis, which implies different enthalpy curves for melting and solidification of the material. Other researchers believe that this is not thermodynamically correct, that the enthalpy curve is unique in both heating and cooling [24], and this is what we found in previous studies [25] of another micro-encapsulated MCP (BASF Micronal 5001 DX) mixed with cement mortar. In the present state of our research, we have not found any other solution than to consider this hysteresis. Having two enthalpy curves for the same material introduces a problem during incomplete melting or solidification since it is necessary to \"switch\" from one curve to the other when the heating or cooling process is reversed. This \"switch\" is not to be underestimated because it can be frequently encountered when the energy gains in the building are not sufficient to completely melt the PCM in the thickness of the coating or when the night temperatures in the building are not low enough to allow the release of all the energy stored during the day by the coating.