## 4 Results and Discussions
### The Influence of Roof Type  
Paraffin was used as the phase change material (PCM) while perlite was chosen to be the sensible insulation material (SIM) for the roofs in the current work because of their similar thermophysical properties for a fair comparison as shown in Table 1. The energy saving characteristics of an ordinary roof (without PCM or SIM), SIM roof, and PCM roof during the summer cooling season were compared. As shown in Figure 4, the magnitudes of the heat flux, \(Q\), for different types of roofs during the air conditioner cooling period are presented. The results indicate that the heat flux, \(Q\), of an ordinary roof increases much more dramatically during the daytime compared with a SIM roof and a PCM roof, which indicates its larger energy consumption. By integrating the heat flux magnitude, \(Q\), with respect to time, \(t\), during the AC working period, the energy consumption of an ordinary roof was  
Figure 2: The temperature variation of Hanzhong city.  
2861.3 kJ/m\({}^{2}\). As a comparison, the heat flux magnitude, \(Q\), of a SIM roof increased more smoothly due to the existence of a SIM layer with a low thermal conductivity, as displayed in Figure 4. For a SIM layer thickness of 30 mm, the energy consumption of a SIM roof during the AC cooling time was 1294.0 kJ/m\({}^{2}\). It means that the energy consumption of the roof decreased by 54.78% when the SIM layer was inserted into the roof compared with the ordinary roof. In contrast to the ordinary roof and the SIM roof, as presented in Figure 4, the heat flux magnitude, \(Q\), of a PCM roof remained constant for a long time under the influence of environmental temperature and solar radiation. As a consequence, when the PCM layer thickness was 30 mm, with a melting temperature of 31, the energy consumption of the PCM roof during the AC cooling time was 1048.3 kJ/m\({}^{2}\), which is 63.36 and 18.99% lower than those of the ordinary roof and the SIM roof respectively. Under this circumstance, it should be concluded that the PCM roof had the best energy saving characteristic during the summer AC cooling time among all the three type roofs.  
To further explain and understand the reason that a PCM roof has the minimum energy consumption during the summer cooling season, the temperature distributions of a PCM roof and a SIM roof (\(D=30\) mm and \(T_{m}=31\) ) during the AC working period are shown in Figure 5. As presented in Figure 5, under the combined influences of the increasing environmental temperature \(T_{e}\) and the solar radiation intensity, \(I\), the exterior surface temperature of the building's roof \(T_{1}\) increased during the daytime and achieved the maximum value at 14:00 p.m. Due to the latent heat characteristic of the PCM layer, the interior surface temperature of the PCM roof (\(x=170\) mm) remained almost unchanged until 16:00 p.m. However, when the PCM layer was fully melted and became a liquid, it behaved like  
Figure 4: Heat flux magnitude of different types of roofs during the summer AC cooling time.  
Figure 3: Iteration process of the roof temperature during the computation.  
the sensible insulation material and lost the latent heat characteristic. Hence, the temperature of the PCM roof interior surface could not be fixed at a relatively constant value and began to increase as shown by the curve at 17:00 p.m. On the other hand, although the low thermal conductivity of the SIM layer could prevent the heat loss to some extent compared with the ordinary roof, its internal surface temperature increased continuously, which actually consumed more energy for the air conditioner to cool down the room than the PCM roof.