## 3 Thermal Balance and Time Constant of a Solid Slab Containing Phase Change Materials (PCM)
Two more roofs, one with high-profile concrete tile having a splotchy terra-cotta finish (SR26E86) and the other one with a high-profile clay tile with cool-colored pigments (SR54E90), were each placed on 3.2 cm thick layer of expanded polystyrene foam (EPS) adhered to the deck using a spray polyurethane adhesive. Three medium-profile concrete tile roofs were configured as follows: (i) direct to the roof deck and the tile painted with a cool-colored pigmented coating (SR37E93), (ii) on battens (\(3\times 4\) cm nominal lumber) with cool-colored pigments (SR37E93), and (iii) on double battens with tile having conventional color pigments (SR10E93). All three medium-profile tiles exhibited less heat transfer across the roof deck as compared with the flat tile (SR13E83) mounted directly to the deck. The medium-profile tile with conventional color pigments and on double battens (0.038 m) showed deck heat transfer very similar to that of the cool-colored tile attached directly to the deck. The terra-cotta tile slightly outperformed all medium-profile tile configurations (Figure 15). Figure 7.1 Field testing of clay and concrete tile roofs on the Envelope Systems Research Apparatus (ESRA). Figure 7.2 Heat flux profiles recorded during the field exposure test of the thermally massive tile roofs containing an above deck thermal disconnect. Thermal performance comparisons of eight test roof assemblies show that in addition to the thermal mass of concrete and clay tiles, the key thermal disconnect measures impacting the magnitude of roof's diurnal peak loads are the following: (i) amount of over-the-deck insulation, (ii) radiative properties of the roof surface, and (iii) the depth of the above-deck ventilation cavity. Two roof designs constructed with high-profile tiles installed on top of a 3.2 cm thick layer of EPS foam demonstrated significantly better thermal performance than the other test roofs. This indicates that, in the case of thermally massive roof tops, the overall thermal resistance of materials and systems installed on top of the roof deck is a key material characteristic affecting the peak load time shift and decreasing the peak heat transfer. As depicted in Figure 15, the additional thermal resistance of EPS foam (RSI-0.85 m\({}^{2}\)-K/W) under the high-profile terra-cotta tile helped shift the time of the peak thermal load by 2 to 3 h, as well as reduced peak heat transfer by over 80% of that measured for the control shingle roof. Even further reductions in deck heat transfer (close to 90%) were observed with the clay tile roof, because its solar reflectance was twice that of the terra-cotta tile. In roof-attic assemblies having additional title floor insulation, the shape of the peak load curve (for roof-generated thermal loads) can be even further flattened and delayed in time, as shown in Figures 8 and 9. In the case of lightweight roof cover materials, for example, asphalt shingles or metal panes, the thermal mass effect can be provided by a layer of PCM installed on top of the roof deck. Following the roof deck design shown in Figures 10 and 11, an unconventional configuration of a metal roof, containing photovoltaic (PV) laminates and a high-performance thermal disconnect system utilizing PCM heat storage, was constructed at ORNL, during the fall of 2009. As shown in Figure 16, a layer of macro-packaged PCM, with a thickness of 1.9 cm, was used. This PCM was placed directly on the roof deck. In this assembly, the organic PCM was packed in arrays of plastic pouches \(4.4\times 4.4\)\(\times\) 1.3 cm with 1.3 cm spacing (air pockets in plastic cells represented about 20% of the total volume). It was followed by a 3.4 cm thick layer of the dense fiberglass insulation with a reflective surface facing the metal panels above, and finally, metal panels with preinstalled PV laminates on top [46]. Bio-based PCM with a melting temperature of approximately 32 \({}^{\circ}\)C was utilized in this experiment. The phase transition enthalpy of the PCM was about 190 J/g.