## 3 Thermal Balance and Time Constant of a Solid Slab Containing Phase Change Materials (PCM)
For the analyzed assembly with a thinner layer of thermal insulation (140 mm), the percent reduction of the heat gains maxima is significant only when the external sol-air temperature amplitude is not too high (up to 25 \({}^{\circ}\)C) as compared with the plain fiber insulation case. Correspondingly, the percent reduction of heat gain maxima and time shifting are less significant. This means that, as compared with roof assemblies containing thicker insulation layers (300 mm), thin cathedral or sandwiched roofs (containing 140 mm layers of thermal insulation) are less effective for controlling peak thermal loads in buildings during the cooling season, even with added PCM. It is also worthwhile noting that increased internal space temperature during the summer (lower temperature gradient across the envelope) increases the magnitude of overall cooling load reductions and, in most cases, peak load reductions. Finally, a comparison of thermal insulation cases with and without PCM (two different thicknesses), indicates that the PCM load is a major factor impacting the time delay in building envelopes. Experimental Analysis of Peak Load Time Shift in Attics Containing PCM-Enhanced Thermal Insulation Installed on the Attic Floor  
During the last two decades, several novel roof structures using PCM-enhanced thermal insulation or other PCM applications have been analysed in laboratory and field exposures. In contrast to earlier PCM studies, where the major interest has been mainly on energy savings, the current work focused on dynamic thermal response characteristics of PCM-enhanced envelopes, and energy savings was one of many results. This included peak load time shifting and reductions of the load maximum values. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Assembly** & **Internal** & **Sol-air ext. Temp.** & **Night ext.** & **Total Cooling Load** & **Peak Load** & **Peak Load Time** \\
**Thickness (m)** & **Temp. (C)** & **Schedule \(T_{ss}\)** & **Temp. min. (C)** & **Reduction (\%)** & **Reduction (\%)** & **Delay (h)** \\ \hline
0.14 & 20 & \(T_{\alpha}\) (c) & 15 & 2.5 & 4.0 & 1.0 \\
0.14 & 20 & \(T_{\alpha}\) (b) & 15 & 2.8 & 8.0 & 2.0 \\
0.14 & 20 & \(T_{\alpha}\) (a) & 15 & 10.8 & 18.0 & 2.5 \\
0.14 & 25 & \(T_{\alpha}\) (c) & 15 & 7.7 & 3.0 & 0.5 \\
0.14 & 25 & \(T_{\alpha}\) (b) & 15 & 10.8 & 6.0 & 1.0 \\
0.14 & 25 & \(T_{\alpha}\) (a) & 15 & 22.0 & 25.0 & 2.5 \\
0.30 & 20 & \(T_{\alpha}\) (c) & 15 & 0.5 & 45.0 & 3.5 \\
0.30 & 20 & \(T_{\alpha}\) (b) & 15 & 7.5 & 51.0 & 4.5 \\
0.30 & 20 & \(T_{\alpha}\) (a) & 15 & 13.6 & 48.0 & 6.5 \\
0.30 & 25 & \(T_{\alpha}\) (c) & 15 & 17.3 & 40.0 & 3.0 \\
0.30 & 25 & \(T_{\alpha}\) (b) & 15 & 35.0 & 65.0 & 5.5 \\
0.30 & 25 & \(T_{\alpha}\) (a) & 15 & 72.0 & 82.0 & 6.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of transient thermal simulations for two thicknesses of envelope assemblies containing dispersed PCM. The following two forms of PCM application were considered: dispersed PCM application blended with different types of thermal insulation and concentrated PCM application in conjunction with the bath fibrous insulation or blown-in attic insulation technologies. Interestingly, the recent work demonstrated that concentrated PCM applications did not have to be directly exposed to the building interior to effectively impact the thermal response of envelopes. Instead, they could be placed inside the roof or wall cavity, as long as phase change temperature was properly selected. A series of dynamic hot box experiments were performed on an attic assembly insulated with loose-fill cellulose, pictured in Figure 7. The attic module was tested under periodic temperature fluctuations in a large-scale climate simulator (LSCS), a large horizontal hot box, at the Oak Ridge National Laboratory [40].