## 4 Methodology and Modeling
### Results for Bioclimate Zone I/ASHRAE 3A (Curitiba, PR)  
Through Figure 8, it is possible to observe the monthly behavior of the Energy Use Intensity with the HVAC systems for the city of Curitiba. Considering the typical meteorological year, it is necessary to use heating, especially in the case of the envelope without any material.  
Highlighting in Figure 8, consumption in winter months (June to September) exceeds consumption in the summer months (December to March). This can be justified by using the heating system through individual thermal resistances at the thermal zones' ventilation terminals. Such equipment has unitary efficiency, making it less efficient than the direct expansion used to cool environments. The central heating system is also required during the winter, increasing energy consumption.  
In comparison with other envelopes, the application of PCM results in an annual EUI that is approximately 82.5% lower during the typical year and, on average, 51.4% lower in future climates. The envelope with thermal insulation, in turn, presents an annual EUI,  
\begin{table}
\begin{tabular}{l r r r r r r} \hline  & \multicolumn{3}{c}{**Curitiba, PR (BZI/3A)**} & \multicolumn{3}{c}{**Rio de Janeiro, RJ (BZ8/1A)**} \\ \cline{2-7}
**Climate** & **NOM** & **INS** & **PCM** & **NOM** & **INS** & **PCM** \\ \hline TMYx & \(-0.144\) & \(0.963\) & \(-0.227\) & \(0.922\) & \(0.885\) & \(0.710\) \\
2050 projection & \(0.945\) & \(0.960\) & \(-0.957\) & \(0.949\) & \(0.918\) & \(0.940\) \\
2080 projection & \(0.967\) & \(0.956\) & \(-0.954\) & \(0.944\) & \(0.906\) & \(0.973\) \\ \hline \end{tabular}
\end{table}
Table 10: Pearson Correlation Coefficients between monthly HVAC EUI and envelope net heat balance: south facade.  
\begin{table}
\begin{tabular}{l r r r r r r} \hline  & \multicolumn{3}{c}{**Curitiba, PR (BZI/3A)**} & \multicolumn{3}{c}{**Rio de Janeiro, RJ (BZ8/1A)**} \\ \cline{2-7}
**Climate** & **NOM** & **INS** & **PCM** & **NOM** & **INS** & **PCM** \\ \hline TMYx & \(-0.150\) & \(0.930\) & \(-0.941\) & \(0.920\) & \(0.856\) & \(-0.969\) \\
2050 projection & \(0.945\) & \(0.950\) & \(-0.984\) & \(0.964\) & \(0.928\) & \(0.923\) \\
2080 projection & \(0.971\) & \(0.950\) & \(-0.988\) & \(0.963\) & \(0.921\) & \(0.983\) \\ \hline \end{tabular}
\end{table}
Table 11: Pearson Correlation Coefficients between monthly HVAC EUI and envelope net heat balance: roof surface.  
Figure 8: Monthly behavior of the EUI with HVAC systems in Curitiba, PR (ZB1/3A).  
\begin{table}
\begin{tabular}{l r r r r r r} \hline  & \multicolumn{3}{c}{**Curitiba, PR (BZI/3A)**} & \multicolumn{3}{c}{**Rio de Janeiro, RJ (BZ8/1A)**} \\ \cline{2-7}
**Climate** & **NOM** & **INS** & **PCM** & **NOM** & **INS** & **PCM** \\ \hline TMYx & \(-0.112\) & \(0.597\) & \(-0.763\) & \(-0.410\) & \(-0.282\) & \(0.794\) \\
2050 projection & \(-0.134\) & \(0.271\) & \(-0.121\) & \(-0.282\) & \(-0.125\) & \(0.815\) \\
2080 projection & \(-0.282\) & \(0.085\) & \(-0.353\)during the TMYx simulation, 75.4% lower than the envelope without material, and the average in future climates is 37.6% lower. When comparing the insulated envelopes with each other, the application of phase change material produces a lower annual EUI: around 3.9% lower in the typical year, 8.2% in 2050, and 10% in 2080.  
Due to temperature increases in climate projections, there is a change in the behavior of energy consumption during the winter period for the building without insulating material in the envelope. In both simulated projections, the winter months have the lowest EUI value of the year; that is, the thermal demand for heating is \"converted\" into thermal demand for cooling. Regarding simulations in which the envelope has either thermal insulation or phase change material, the monthly energy consumption profile is similar and very close throughout the year for the TMYx climate. The \"detachment\" of the consumption curves is notable in the months outside the winter period in future climate projections, with a difference of almost 1 kW h m\({}^{-2}\) in 2080.