## 3 Thermal Balance and Time Constant of a Solid Slab Containing Phase Change Materials (PCM)
All test modules had softin-to-ridge attic ventilation with vent area-to-attic floor area ratio of 1:300. [40]. Test attics were equipped with arrays of 50 or more thermocouples and heat flux transducers embedded in the roof deck and in the attic floor for measuring temperature profiles and heat flow rates across the roof and attic. The first roof with localized PCM was built in 2004. At that time, the main interest was in roof surface materials, overall roof thermal resistance, optical characteristics of the roof surface and roof deck components, and the resulting reductions of thermal loads. Thermal response characteristics, such as peak load shifting, were not of primary interest. This earliest PCM roof configuration had aluminum foil faced pouches of inorganic PCM that were installed directly on top of the roof deck, as shown in Figure 10b. The first week of testing demonstrated greater than 90% reduction of the daily peak thermal load as compared with a conventional shingle roof [40]. Unfortunately, as shown in Figure 10c, the pouch design was not planned for roof-top applications and PCM leaks occurred. A second example of a PCM roof contained organic PCM. It was based on a \"cool roof\" design, similar to the roof shown in Figure 10. Some of the test data that focused on the reduction of the thermal load generated by the roof has already been published [40; 45]. Figure 11 shows the analysis of the peak load time shift for a cool metal roof containing PCM. Performance comparisons are also made for a similar cool metal roof with no PCM and with two conventional slope roof configurations using conventional control shingles and cool shingles. The second PCM roof contained three layers if 2 mm thick localized PCM. Specifically, PCM-enhanced polyurethane (PU) foam and two layers of PCM-impregnated fabric were installed above the roof deck. Following the detailed thermal simulations of roof temperatures, the melting point of the PCM dispersed in the PU foam was 26 \({}^{\circ}\)C, whereas that for the fabric was 32 \({}^{\circ}\)C. The total heat storage potential of the PCM assembly (for a total of five layers) was around 15 Wh/m\({}^{2}\). Both of the roofs with PCM had top surfaces with solar reflectance of 0.26 and thermal emittance of 0.81, air ventilation cavities, and radiant barriers. One of the conventional shingle roofs was covered with cool asphalt shingles with solar reflectance of 0.27 and thermal emittance of 0.86. The cool shingle roof was used as a control for comparison with the thermal performance of the prototype roof systems. All three roofs had very close to the same radiative properties. A fourth shingle roof had conventional shingles and provided another opportunity for comparison. The conventional shingles had solar reflectance of 0.09 and thermal emittance of 0.89. Data in Figure 11 show that both advanced metal roofs with above deck ventilation, and attic radiant barriers, significantly reduced the peak hour thermal loads as compared with the cool shingle attic. This reduction was about 31% in the case of no PCM metal roof without PCM and 35% for the metal roof with PCM. Performance comparisons were also made for the conventional dark shingle roof (SR09E89). In this case, the reduction of roof deck maximum daily heat flux for the PCM roof,  
Figure 10: PCM roof testing at Oak Ridge National Laboratory. (**a**) South facing array of test attics, front view; (**b**) Installation of foil pouches with inorganic PCM on top of the roof deck insulation, visible over the deck ventilation channel; (**c**) Leaking pouches with inorganic PCM. was about 75% [40; 45]. This specific roof assembly initiated a series of subsequent roofing experiments using different configurations of roof-top materials, conventional thermal mass, or PCMs, as well as a variety of roof deck ventilation and thermal insulation options [40]. As shown in Figure 11, the PCM roof provided a notable shift in the time of the peak thermal load.