## 3 Thermal Balance and Time Constant of a Solid Slab Containing Phase Change Materials (PCM)
In addition to the attic insulated conventional cellulose insulation, two loadings of microencapsulated PCM with a melting point at approximately 27 \({}^{\circ}\)C and phase change enthalpy of approximately 120 kJ/kg were tested in blends with cellulose (5% and 20% by weight, and approximately 0.8 to 1.0 kg and 3.0 kg of PCM per m\({}^{2}\) of roof assembly). The insulation thickness was 33 cm. The main focus of the attic tests was the PCM discharging time (solidification). PCM charging (PCM melting) is quite intensive and fast in attics, because of the rapid morning increase in temperature caused by the sun. However, the attic cooling process is significantly slower. In a well-designed PCM application, during the night, 100% of the PCM should fully discharge before morning. During the dynamic LSCS tests, the attic was subjected to changes of temperature to 21 \({}^{\circ}\)C for about 16 h, rapid temperature ramps to 49 \({}^{\circ}\)C or 57 \({}^{\circ}\)C, and exposure to 49 \({}^{\circ}\)C or 57\({}^{\circ}\)C for about 4 h, followed by natural cooling back to 21 \({}^{\circ}\)C. The array of thermocouples installed at 2.5 cm intervals was used to monitor the temperature distribution across the layer of insulation with a 33 cm thickness. Figure 8 shows temperature profiles recorded during the dynamic hot box experiment performed on the attic containing 5% PCM-insulation blend. For two thermal excitations of 28 \({}^{\circ}\)C and 36 \({}^{\circ}\)C, the time delay between the peak temperature on the top surface of the attic insulation and thermal response on the attic ceiling surface (bottom of the structure) was between 2.5 and 3.0 h. Another interesting finding from this analysis was that, due to specific selection of the PCM phase transition temperature, only insulation layers located higher than 10 cm from the attic floor were involved in the phase changing processes. It took about 6 to 10 h to fully discharge the energy stored in these layers. This experiment provided evidence of PCM charging and discharging even in the attic configuration containing only 5% PCM blend (with the approximate load of microencapsulated PCM around 1.0 kg/m\({}^{2}\) of the attic floor area). Figure 7: Large-scale climate simulator (LSCS) box test module (**left**); PCM-enhanced cellulose insulation (**right**). A similarly constructed attic was tested in field conditions at Oak Ridge National Laboratory [40; 41]. The attic footprint was about 4.9 m long by 1.5 m wide. Its shed roof faced directly south. The roof slope was 1 in 3 cm (18.4\({}^{\circ}\)). The test attic contained loose-fill fiberglass insulation on the attic floor, and layers of PCM-fiberglass mixtures were placed on top. As shown in Figure 9, the full-scale test attic contained about 25 cm of blown fiberglass insulation with a density of 29 kg/m\({}^{3}\). Next, on top of this insulation, four layers of the PCM-adhesive blend, each with a thickness of 1.3 cm, were installed with a layer of blown fiberglass, with a thickness of 1.3 cm, installed in between each layer of PCM-adhesive blend. The thickness of the added PCM-fiberglass multilayer sandwich was approximately 11 cm, giving the total attic insulation a thickness of 36 cm. The PCM melting temperature was at 29 \({}^{\circ}\)C and the phase transition enthalpy was approximately 170 J/g (110-120 J/g after encapsulation). The approximate load of the microencapsulated PCM for this application was between 4 and 5 kg/m\({}^{2}\) of the attic floor area, which yielded a heat storage density of approximately 120 to 170 W/m\({}^{2}\). In this field experiment, an advanced attic configuration was used. In addition to PCM, it contained above-deck ventilation and a metal roof surface with high solar reflectance (a cool roof, SR28 and TE81).