## 6 Conclusions  
This paper has presented a new numerical model to analyze the thermal behavior of a composite material integrating a bio-based micro-encapsulated PCM. This model has been developed by using the heat flux and temperature from measurements performed with the LGCgE experimental fluxmeter bench. Coupled with an inverse method, these data have allowed characterizing the parameters of the proposed numerical model.  
Through this model, the thermodynamic analysis of the PCM is based on the enthalpy equations of a binary solution, associated with the equations of Gumbel's Law. The latter serves to numerically describe the complex phenomena generated not only by supercooling during the material's solidification phase but also by the presence of several components with distinct thermal behavior within the same PCM. The hybrid model developed during this work was coupled to inverse methods in order to characterize the thermophysical properties of a bio-sourced gypsum plaster incorporating a vegetable oil-based PCM, intended to improve the energy efficiency of buildings. An experimental error analysis was performed to evaluate the accuracy of this characterization, and verifications were carried out on model reliability according to various thermal dynamics and in the case of partial melting or solidification. Given the results obtained, the following conclusions could be drawn:  
* This new hybrid model, associating the enthalpy of a binary solution with Gumbel's Law equations, succeeds in describing the thermal behavior of the studied composite material (gypsum board + micro-encapsulated PCM) with high accuracy even when subjected to undercooling.
* The various dynamic thermal loads (ramps) between 10\({}^{\circ}\) and 30 \({}^{\circ}\)C depict the different thermal behaviors well represented by the hybrid model. The energy balances performed between these two temperature levels show a good level of repeatability and measurement accuracy.
* This model also takes into account the partial melting/solidification of the PCM, which can occur during its use in a building subjected to meteorological constraints.
* The model has successfully characterized the thermophysical properties of the coating incorporating PCM and, in particular, the latent heat contained in the material. By knowing that the coating is loaded with 70% PCM and in comparison, with the DSC measurements conducted by the manufacturer, the latent heat identified by characterization could be verified.
* An error calculation was used to determine uncertainties of around 4%, which appears acceptable for our application.  
A subsequent work program would call for integrating this new hybrid model into a building simulation model in order to predict the energy performance of this type of coating.  
Conceptualization, H.T., P.T., L.Z., Y.C., H.L.; methodology P.T., L.Z., H.T., Y.C., H.L.; investigation, H.T., P.T., L.Z., Y.C., H.L.; data curation, H.T., P.T., L.Z.; writing-editing, H.T., P.T., L.Z., H.L; funding acquisition L.Z, H.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the University of Artois and MCI Technology company.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.