## 4 Methodology and Modeling
### Results for Bioclimate Zone I/ASHRAE 3A (Curitiba, PR)
#### 5.1.1 North Facade (Thermal Zone 3)  
Figure 9 illustrates the net heat balance on the inner face of the surface (\(Q_{net}\)), resulting in monthly heat gains by the thermal zone when the balance is positive or heat losses by the zone when the balance is negative. It is observed that, for all simulations, the heat balance on the surface with the phase change material is always negative, denoting a net heat loss from the thermal zone during its occupation, which reduces the monthly cooling load. During the winter months, especially in Figure 8a, energy consumption for this envelope decreases, which does not mean that there is a demand for heating, but instead that the thermal zone, through solar gains and internal loads, together with thermal insulation, manages to maintain comfortable temperature levels passively. In this sense, the temperature of the internal face can remain close to the material's solidification temperature. In contrast, its core and mainly, the external face of the facade have lower temperatures, which reduces the heat transfer rate through this surface. The envelope without any material does not show characteristic behavior during the typical meteorological year, having one of the lowest values for the heat balance in June (2 kWh/m\({}^{2}\)), the month with the highest EUI of 4 kWh/m\({}^{2}\). In October, outside the intense cold season, during spring, this envelope has the lowest value for the heat balance (3 kWh/m\({}^{2}\)), and, consequently, one of the highest EUI recorded for this envelope (3 kWh/m\({}^{2}\)). The absence of insulating material causes intense heat gains in the future climate's simulations, frequently exceeding 5 kWh/m\({}^{2}\) and 8 kWh/m\({}^{2}\) per month, reaching maximums of 8 kWh/m\({}^{2}\) in March 2050 and 10 kWh/m\({}^{2}\) in May 2080, possibly due to the intensification of direct solar irradiation during this period. The application of the resistive thermal insulator guarantees the maintenance of low levels of heat gains and losses throughout the year, as observed in all simulations. Figure 9: Monthly net heat balance across the north facade in Curitiba, PR (ZB1/3A). The hourly curves of mean radiant temperature (\(T_{mr}\)) and conduction heat flux on the inner face of the envelope surface (\(q_{int}^{\prime\prime}\)) for Thermal Zone 3 are expressed in Figure 10. The positive direction of heat flux indicates a flow from the outside to the inside of the thermal zone. For Curitiba, we chose to study the profile of the variables in the typical winter week, defined between 8 and 15 July, according to the location's TMYx climate file. Simulations with phase change material in the envelope, for the typical meteorological year, result in mean radiant temperatures higher than other envelopes, especially among the working periods on weekdays, with a weekly average of 24.06 \({}^{\circ}\)C. During the typical week (Figure 10a), atnight, conductive heat flow in the envelope with PCM is positive or very close to zero, contrasting with other applications, in which the heat flow is negative. In this sense, thermal zone 3 loses heat at a lower rate or even receives heat in this interval of hours through the external wall. This passive behavior is complemented by the heat removal during the day due to the PCM, reducing the temperature range. Thus, when the building returns to operation the following day, the thermal zone presents a higher mean radiant temperature. Consequently, its thermal heating load decreases, especially at the beginning of occupancy. The material stores heat from the thermal zone during the day and releases it back during the night. The weekly mean radiant temperature is 24.85 \({}^{\circ}\)C in the 2050 projection and 25.14 \({}^{\circ}\)C in 2080 over the occupied period.