## 4 Methodology and Modeling
### Results and Discussion  
A total of 18 simulations were carried out: nine simulations for each bioclimatic zone, divided into simulations varying the composition of the envelope (resistive thermal insulation, phase change material, and uninsulated) for each of the climate files (original TMYa, 2050 projection, and 2080 projection). The morphing process was executed using the C@WorldWeatherGen tool, generating climate files for the representative years 2050 and 2080 from the TMYa. The average duration of simulations using EnergyPlus with insulated or uninsulated surfaces was approximately 30 to 35 min, while the phase change material simulations lasted for an average time of roughly 40 to 45 min. The simulations were performed using an i5-8250U processor and 8 GB of DDR4 RAM. Metrics for the entire building and representative thermal zones are evaluated. The thermal zones and spaces selected for analysis are zone 1 (south facade) and zone 3 (north facade) on the middle floor, both occupied and air-conditioned, and the return plenum on the roof. Inspired by the literature [46], the monthly net heat balance \(Q_{net}^{m}\) is presented for each of the simulated climate behaviors, to evaluate, particularly, the impact of facades' orientation: it expresses the sum of the hourly-mean conduction heat flux on the internal face of the surface \(q_{int}^{\prime\prime}[h]\) for a given month \(m\), during occupation hours  
\[Q_{net}^{m}=\sum_{Hhours}\frac{q_{int}^{\prime\prime}[h]}{1000} \tag{16}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Roof**} & \multicolumn{2}{c}{**External Wall**} \\ \cline{2-5}
**Bioclimatic Zone** & \(R\) [**m2K/W**] & \(e\) [cm] & \(R\) [**m2K/W**] & \(e\) [cm] \\ \hline
1 (3A) & 4.319 & 17 & 1.903 & 8 \\
8 (1A) & 3.472 & 14 & 1.037 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Thermal resistance used in each model and material thickness. Figure 7: Detailing of surface constructions, out of scale. The metric results in monthly heat gain or loss during the hours of building and HVAC system operation. The hourly data of mean radiant temperature, operative temperature, and heat flux through the envelope are assessed during typical weeks defined by the TMYx climate files (weeks with mean temperatures closest to the mean for each season). Unlike the operative temperature, we chose to use the mean radiant temperature to evaluate thermal zones 1 and 3, as the environments are conditioned. Therefore, the average air temperature approaches the setpoint and does not illustrate the direct impact of the envelope as desired. In parallel, the operating temperature of the plenum is investigated, as this environment only has opaque surfaces and is not conditioned but receives return air from the thermal zones. Emphasizing the phase change materials applications, the PCM's physical state is illustrated on an hourly basis through two behaviors defined as \"characteristic\" and \"predominant\". EnergyPlus generates an output for each node's state comprising a continuous value between \(-2\) (liquid) and 2 (solid). Utilizing the Mean Value Theorem, a representative (characteristic) numerical value for the whole material is extracted from Simpson's Integration Rule using all node values. The predominant state is the mode of the nodal results. Building-wise, the total monthly energy consumption with the modeled HVAC system is extracted and divided by the conditioned floor area, a metric represented by Energy Use Intensity, or EUI, intending to incorporate the partial load profile that air-conditioning equipment can have. Tables 7 and 8 summarize the results of the annual EUI with the HVAC systems for each of the envelopes in the simulated climate scenarios. The acronyms \"NOM\", \"INS\", and \"PCM\" represent the three envelope configurations: uninsulated (no material applied), resistive thermal insulator, and phase change material, respectively.