## 6 Application of the Model  
The preliminary activity led to the validation of the model's capability of performing a numerical simulation of the dynamic behavior of a typical wall, in circadian transient conditions. For this reason, the model was used to investigate an interesting case study. A typical single-zone building was selected in order to investigate the performance and capabilities of the developed model. The building had the features of a typical residential building located in the surroundings of Genoa, Italy. The apartment was in the middle of a three-floor building. In addition, the \"single-zone\" had two walls in common with other neighbors and two different ones facing outwards that were exposed to the external air and to solar radiation. Two cases will be studied in the following: The first one takes into consideration a period of one week, made up of seven different daily profiles of temperature with circadian oscillations; while the second one analyzes the thermal behavior of a leisure house (i.e., used, for example, on weekends only), for different powers of the heaters and for different outdoor temperatures, in order to analyze and speculate about the possibility of saving energy by means of remote control of the plant. The sketch of the single zone is shown in Figure 13 and the general conditions, dimensions, and boundary conditions are shown in Table 4.  
Thermal properties of the exterior, internal walls, roof, and floor are presented in Tables 5-8 (where a code is indicated, it refers to the standard UNI/TR 11552:2014 [42]). Four pie charts are displayed, in Figure 14, in order to summarize the common configuration of the considered single-zone building. They describe the thermal properties of the various parts of the building. It is possible to deduce that each part had a different weight in the various physical processes. For instance, the maximum weight of thermal capacity was accounted for by the roof and floor, while most of the surface area was allocated to the exterior wall. In order to investigate the application of the developed model, another case study was generated. In this study, an insulation layer with embedded PCM was used for all the surrounding walls. PCMs are well-known as a new generation of insulating materials, applied in order to absorb the daily energy and then release it at night. In previous studies, authors deeply studied, both experimentally and numerically, the use of PCMs [11; 12; 43; 44]. Figure 15 shows the schematic of the building's embedded PCM; in this model the PCM was placed close to the inside layer of the walls. The outside temperature and the characteristics of the used PCM are shown in Figure 16 and Table 9.  
In this model was also taken into account the hysteretic behavior of PCMs, already deeply described in references [11; 12] and [43; 44], in order to achieve accurate results in a proper time. In this way, the energy consumption of the single-zone house was obtained. Figure 17 illustrates the amount of energy consumption for 10 days in the building in two different cases:  
(1) Without PCM insulation;  
(2) With a PCM insulation layer. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Materials** & **Thickness (m)** & **Density (kg/m\({}^{3}\))** & **Thermal Conductivity (W/m\(\cdot\)K)** \\ \hline Exterior plaster & 0.02 & 1000 & 0.9 \\ Brick & 0.10 & 2000 & 0.281 \\ Interior plaster & 0.02 & 1000 & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Thermal properties of interior wall layers. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Materials** & **Thickness (m)** & **Density (kg/m\({}^{3}\))** & **Thermal Conductivity (W/m\(\cdot\)K)** \\ \hline Interior & 0.015 & 1700 & 1.47 \\ Cement & 0.02 & 2000 & 1.4 \\ Lightweight concrete & 0.12 & 1400 & 0.58 \\ Cement & 0.02 & 2000 & 1.4 \\ Brick-block concrete & 0.24 & 900 & 0.69 \\ Interior plaster & 0.02 & 1800 & 0.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Thermal properties of roof layers, SOL02 [42].