## 4 Methodology and Modeling
### Phase Change Material Selection and Simulation Setup  
The energy model used has heating and cooling setpoint values of 21 \({}^{\circ}\)C and 24 \({}^{\circ}\)C, respectively, representing temperatures commonly used for activating HVAC systems. The selection of the phase change material respects these limits, aiming to store thermal energy at an appropriate temperature for both the HVAC system and the building's occupants, and thus, standardizing the material in different climates is possible. For this logic and taking as a reference the selected materials and results in some of the previously described works [16; 20; 21], the SP24E inorganic PCM, produced by RubiTherm [41], was chosen, mainly because of the coincidental material's operating range of temperatures and the HVAC setpoints. The manufacturer mentions that, for application in buildings, inorganic materials are generally preferred [42]. The PCM in question presents other favorable characteristics for its selection: stable performance during phase change cycles, high latent heat per unit volume, limited subcooling, and low flammability. It is non-toxic and can be macroencapsulated. The PCM data used for the simulations can be seen in Table 5.  
The selected PCM is modeled in EnergyPlus using class _MaterialProperty:PhaseChangeHistresss_, capable of modeling the cyclic behavior of the latent phase of materials. The class requests properties of both physical states, described in Table 5. To do so, it is necessary to use the CondFD finite difference algorithm. Due to its robustness and stability [29], the fully implicit scheme is used, such as the TARP algorithms for internal convective exchanges and the DOE-2 for external convective exchanges. As discretization parameters, the values of 0.3 for the space discretization constant and 60 time steps per hour, the maximum allowed by EnergyPlus, were used [43]. Such algorithms and configurations are not necessary for simulating envelopes without PCM but are maintained in favor of standardizing the numerical methodology between simulations. Tolerances for numerical convergences were kept as the software default values.  
The thickness of the PCM used on each surface is equivalent to the thickness of the insulation applied in each of the respective facade systems since the aim is to replace one with the other geometrically. According to the models [33], the thermal resistances (\(R\)) of the insulators used in each envelope are visible in Table 6.  
It should be noted that, in the energy models, insulators are represented only through their thermal resistance values, without the definition of physical material, that is, without thermal mass. Fiberglass, mineral wool, and cellulose are among the most common thermal insulation materials used in civil construction [44], which have a similar thermal conductivity (\(k\)) and can be approximated by 0.04 W/mK [45]. The theoretical thickness (\(e\)) of the insulating material is given by multiplying the thermal resistance (\(R\)) and the thermal conductivity of the same material (\(k\)). This thickness is also the thickness of the PCM that will replace the insulator.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Property** & **Value** & **Dimension** \\ \hline Melting temperature interval & 24–24 (peak at 24) & \({}^{\circ}\)C \\ Freezing temperature interval & 23–21 (peak at 21) & \({}^{\circ}\)C \\ Latent heat (\(L\)) & 150 & kJ kg\({}^{-1}\) \\ Specific heat (\(c_{p}\)) & 2 & kJ kg\({}^{-1}\) K \\ Solid state density (\(\rho_{sol}\)) & 1600 & kg m\({}^{-3}\) \\ Liquid state density (\(\rho_{liq}\)) & 1500 & kg m\({}^{-3}\) \\ Thermal conductivity (both phases) (\(k\)) & 0.5 & W m\({}^{-1}\) K \\ \hline \hline \end{tabular}
\end{table}
Table 5: SP24E data.  
In the case of the non-insulated simulated envelopes, it is important to stress that it is not a cavity with a void between its layers: for this research, an uninsulated envelope is a construction with the absence of insulating material, and the adjacent layers are close to each other, without any gaps.