## 3 Thermal Balance and Time Constant of a Solid Slab Containing Phase Change Materials (PCM)
The large amounts of solar energy collected by the roof surfaces result in rates of heat transfer to the interior, that must be removed by the space conditioning systems to maintain occupant comfort. Unfortunately, these loads are the greatest during afternoon hours, which is the time when the peak of the building energy consumption occurs. Therefore, from a peak energy management perspective, it is critical to minimize the roof generated loads and, if possible, shift the maximum heat gains to later hours in the night. Usually, large amounts of conventional thermal insulation are used for this purpose. Quite often, the effectiveness of this approach is compromised by the existing thermal bridging or a lack of space for thermal insulation. Furthermore, as discussed in earlier sections, lightweight thermal insulation does not create significant peak load shift. An earlier research on different designs of attics and roofs by [PERSON], [PERSON] et al. [30; 40; 45] demonstrated that a combination of thermal disconnect systems installed on the roof deck level and attic floor insulation can effectively reduce and shift peak thermal loads. Thermal disconnect systems installed over the roof deck can effectively control the roof surface and roof deck temperatures [28]. The thermal performance of the previously described metal PV-PCM roof, presented in Figure 16, was monitored through several seasons and compared with a traditional shingle roof and differently constructed metal roofs using reflective cool coatings [44; 46]. As shown in Figure 19, the summer maximum roof surface temperature can be as high as 80 \({}^{\circ}\)C. At the same time, the maximum temperature of the underside surface of the roof deck can be 40 \({}^{\circ}\)C lower than the surface temperature. In this roof, the first component of the thermal disconnect system, which works as a thermal break and provides above-deck ventilation, is the 5.7 cm thick air containing a radiant barrier. For comparison, the peak time temperature on top of the layer of thermal insulations (dense fiberglass installed just behind the air cavity and over the PCM) is about 10 \({}^{\circ}\)C lower than that measured on the exterior roof surface. Figure 7.6 Example of summertime temperature distribution in a sloped metal roof with integrated PV laminate and containing thermal disconnect system utilizing PCM, air ventilation cavity, radiant barrier, and over-the deck insulation, as presented in Figure 7.7  
In the second example, the effectiveness of a thin roof-deck-installed thermal disconnect technologies (only about 1 cm and 2.5 cm, with included PCM heat storage) was evaluated with three roofs studied, during 2011, in Albuquerque, New Mexico. The system studied was comprised of the following: (i) the cool roof surface, (ii) the PCM heat storage, and (iii) the board with micro air channel installed directly on the roof deck. As depicted in Figure 20, three test roofs were used for these performance comparisons. Each of these three roofs covered built-alike test hut. Test roofs were similarly constructed with the following differences in layers installed on top of the roof decks:  
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2. Hut 1 was a control hut built with a typical slope roof covered with conventional dark shingles (SR09E90) installed directly on the roof deck (over a typical roofing underlayment). Roof deck assembly R-value was 0.14 m\({}^{2}\)K/W. 3. Hut 2 had a typical slope roof covered with solar reflective shingles (SR25E86) and built with a 1 cm thick layer of PCM board that contained about 2.5 to 3 kg/m\({}^{2}\) PCM, melting point was 28 \({}^{\circ}\)C, and energy storage density of the PCM board was around 90 Wh/m\({}^{2}\). The PCM board was installed over a 1 cm thick composite board with air channels (for thermal break and roof deck ventilation), which was attached to the roof deck. Roof deck assembly R-value was 0.39 m\({}^{2}\)K/W. 4.