## 4 Conclusions  
The goal of this work is to present an efficient method for characterizing the thermo-physical properties of a composite material, which is in the present case a cement mortar containing a micro-encapsulated PCM, as it could be used in real conditions. These properties are the required parameters for the development of a numerical model able to reliably representing the thermal behavior of the material containing phase change material. The first step of the study is based on an experimental device where the material to be characterized is repeatedly stressed by temperature ramps, at various speeds, in order to carry out several cycles of melting/crystallization of the PCM. This fluxmetric device allows simultaneous measurements of heat fluxes and temperatures to the access faces of the material during these successive thermal stresses. These non-intrusive measurements, essential for the characterization of the composite material, are then used as boundary conditions of a numerical model detailed hereafter. In a second step, a physical model is developed to reproduce both the thermal and thermodynamic behavior of each sample. In practice, it is thus necessary to impose a thermodynamically consistent formulation of the enthalpy \(h(T)\), represented in the present case as a binary solution. This function \(h(T)\) implemented in the numerical model, developed in a finite-volume framework, makes it possible to account for the non-symmetrical thermal response of the samples submitted to heating and cooling stresses (i.e., fusion and solidification). The last step is to combine together in an inverse method the experimental measurements with the numerical results obtained when solving the physical model. The use of efficient optimization methods allows a reliable estimation of the thermo-physical properties of the composite material, integrating the accuracy of the experimental measurements, and the thermodynamical correctness of the modeling. These thermo-physical parameters stand here for the thermal conductivities and heat capacities when the PCM is in the solid or liquid state on one hand, and the temperatures defining the transition range and the corresponding latent heat on the other hand. Concretely, the identification of the parameters is done simultaneously for each of the three cycles and then altogether with the inversion method. In order to thoroughly test the method, the studies are conducted on several melting/solidification cycles for three mortars incorporating different amounts of PCM. The results obtained show a very low dispersion, less than 3% and 4% for thermal conductivities and heat capacities, respectively, 2% (0.5K) for \(T\), 3% for \(L_{M}\), and 4% for the complete enthalpy curve. These results are excellent considering the current standards, which are usually advanced as 1K for \(T_{M}\) and 10% for \(L_{M}\)[66; 67]. Moreover, the masses of PCM integrated in the mortar as well as the speeds of thermal ramps do not affect the estimate of the transition temperatures, depending solely on the nature of the PCM which is similar from one sample to another. This independence is obviously in accordance with the laws of thermodynamics. In addition, by taking into account the thermal contact resistances between the sensor and the samples, different from one side to another and dependent on the surface finishing and assembly (i.e., variable of a sample to another), do not pose any difficulty but, more importantly, improves the accuracy of the results. In contrast, if ignored, it would be equivalent to a direct method, and consequently, the estimated thermal conductivities would be erroneous. Concerning the prospect of this work, it concerns the studies of more complex PCMs which cannot be described by a binary model but need more sophisticated thermodynamics. This could finally be one of the main limitation of the present method since it can only determine the values of already known parameters.