## 3 Studies of PCMs Incorporated in Passive Systems
### Experimental Studies
#### 3.1.3 Dynamic Numerical Simulations of Buildings Incorporating PCMs  
Numerical modeling and simulation of PCMs embedded in building envelopes are very useful for building design and optimization. In most numerical studies, commercial software, such as EnergyPlus, TRNSYS, MATLAB, COMSOL, and ANSYS Fluent, are used to solve the energy equations and to perform numerical simulations under varying weather conditions [17]. The main objective of these simulations is to study and optimize the effect of the integration of PCMs in the walls of buildings, their position in the walls, their thermo-physical properties, such as melting temperature, thermal conductivity, and the effect of their thickness. [PERSON] et al. [114] studied composites based on standard mortar and two commercial micro-encapsulated paraffin PCMs with melting temperatures of 23 and 26 \({}^{\circ}\)C, respectively. Several percentages of PCMs were used and the performance of the resulting composites was experimentally tested. These experimental data were used to validate a numerical model developed on COMSOL Multiphysics. The numerical model is based on a one temperature formulation and considers that the PCM and the mortar constitute a homogeneous medium. A parametric study was conducted to propose a method to optimize the choice of the melting temperature of the PCM. Using the climatic conditions of Messina in Italy, the authors obtained an optimal temperature of 27 \({}^{\circ}\)C. The results also showed that the addition of 15 wt% of PCMs increases the thermal comfort conditions by about 15% compared to the reference case composed of pure mortar (without PCM) based on the American standard ASHRAE 2017 [115]. [PERSON] et al. [116] conducted a parametric study on the factors influencing the performance of PCM-based wallboard applied on the interior and exterior faces using the effective heat capacity method to describe the phase change. The exterior wall is subjected to a periodic boundary condition and solar radiation. Thermal properties, such as melting temperature, phase change range, enthalpy of fusion, thermal conductivity, and heat exchange coefficient, were optimized based on two criteria: interior surface temperature and diurnal thermal energy storage. The optimal melting temperature of the PCM embedded in the interior wall is equal to the interior ambient temperature without taking into account the internal heat gains. The melting temperature of the exterior PCM wall depends on both the interior and exterior environments, although the impact of the exterior environment is reduced due to the exterior insulation. Walls containing PCM show the best results if the PCM melts completely over a full daily cycle. Moreover, the parametric study showed that the thermal conductivity of the PCM has a low impact on the results. [PERSON] et al. [117] examined, through a numerical study, the effects of adding microencapsulated PCMs to concrete based on four criteria: PCM mass fraction, enthalpy of melting, phase change temperature, phase change range, and external temperature. The simulations were performed considering two walls: one heterogeneous and one homogeneous. The difference between the simulation of the heterogeneous and homogeneous walls is less than 2%, which shows that the heterogeneous composite can be treated as a homogeneous material with a volumetric thermal capacity and an effective thermal conductivity. The rest of the simulation was therefore performed with a homogeneous model. The main results are as follows:  
* the addition of micro-encapsulated PCM and/or the increase of the PCM melting enthalpy reduced and delayed the thermal load of the building,
* the melting temperature of the PCM should be close to the indoor temperature regardless of the climatic conditions,
* the phase-change temperature range had limited effect on energy flux reduction and time shift.