## 3 Thermal Balance and Time Constant of a Solid Slab Containing Phase Change Materials (PCM)
This time shift was about 1.5 h as compared with a shingle roof with similar surface radiative properties. However, the peak load time shift was over 3.5 h as compared with the roof using conventional non-reflective shingles. Bear in mind that this time shift was based on the roof deck surface temperature. Therefore, in the case of the complete roof assembly, or roof plus attic design, the time shift generated by the entire roof structure could be appreciably higher depending on dynamic impacts of the attic floor insulation and other construction components. Following the roof designs described in Figures 10 and 11, several similar roof configurations were developed with significantly higher energy storage potentials [45]. The experimental roofs utilized both organic and inorganic latent heat storage products. All of them, in addition to substantial reductions of peak thermal loads (around 90%), demonstrated noticeable peak load time shifting. Another roof configuration of roofing containing localized PCM and micro-ventilated air channels was recently demonstrated in Albuquerque, New Mexico where two insulated near-identical wood-framed test huts were monitored in field conditions. One of these huts contained a sandwich of the PCM board and microchannel boards (for roof ventilation purposes) on the roof deck. The PCM layer was one cm thick and contained about 2.5 kg/m\({}^{2}\) of PCM with melting point 28 \({}^{\circ}\)C (determined with use of a series of transient finite difference thermal simulations). The energy storage capacity of the PCM board was ~90 Wh/m\({}^{2}\). All other structural components of the attics and walls were installed and insulated the same as follows:  
1. non-PCM hut-dark roof shingles (solar reflectance of 0.05 and a thermal emittance of 0.90 (SR05E90);
2. PCM hut-cool shingles (solar reflectance of 0.25 and a thermal emittance of 0.86 (SR25E86);  
Figure 11: Roof assembly details and heat flux profiles recorded during the field exposure test of a metal roof containing PCM-enhanced impregnated foam and fabric. 3. on the ceiling, on top, a R-3.7 (m\({}^{2}\)-K/W) layer of attic fiberglass insulation and, under, a R-2.3 (m\({}^{2}\)-K/W) layer of fiberglass;
4. inside the wall cavities, a R-2.3 (m\({}^{2}\)-K/W) layer of cavity fiberglass three cm from the internal surface of cavities. The amount of thermal insulation was the same in both test huts. Furthermore, the test huts had approximately the same air-leakage rates as confirmed by blower door testing. As shown in Figure 12, the PCM roof exhibited about a 20 \({}^{\circ}\)C lower maximum roof deck temperature as compared with the roof with conventional low-reflective shingles. This indicated that less heat was transmitted to the interior of the building. An analysis of time shifts due to PCM changes in the temperature profiles showed that most peak load time shifts in roofs containing PCM were generated by the PCM. A four-hour long peak-load time shift could be created by a layer of PCM and a 1 cm thick thermal insulation (approximately R\({}_{\text{SI}}\) = 0.15 m\({}^{2}\)-K/W) installed on top of the roof deck, as shown in Figures 12 and 13. A proper selection of the PCM's phase transition temperature is crucial. It must be consistent with the expected roof deck temperatures [44]. Figure 12: Peak load time shift between conventional shingle roof and PCM roof. Figure 13: Temperature profile across the roof containing PCM board. Impact of Dynamic Thermal Disconnect Systems and Roof R-Value on the Reduction of Peak Thermal Loads  
Reduction of peak thermal loads generated by building envelopes is one of the primary challenges associated with building design, second only to the shifting of the peak load time. As depicted in Figures 5 and 6 and listed in Table 2, PCM can shift the time when the peak thermal loads occur. However, the reduction of the peak load value is also directly dependent on the amount of thermal insulation used, expressed by the envelope assembly's R-value.