## 3 Results and Discussion  
### Comparison of Surface Temperature of Four Internal Wall Configurations  
To observe the dynamic thermal behavior of four internal walls for different heating durations, Figure 6 shows the variations of inner surface temperature \(T_{\text{in,i}}\) of the internal walls, taking heating duration of 1 and 8 h as examples.  
It is found in Figure 6 that at the starting time of heating cycle, the \(T_{\text{in,i}}\) of Wall 4 (insulted with XPS) is increasing rapidly at the beginning of the heating period, and then fluctuates at 16 \({}^{\circ}\)C,  
Figure 5: Validation of temperature distribution in a thermal mass: (**a**) Point-1; (**b**) Point-2; (**c**) Point-3; (**d**) Point-4.  
Figure 6: Variations of inner surface temperature \(T_{\text{in,i}}\) of the internal walls with time: (**a**) \(C_{\tau=1}\), (**b**) \(C_{\tau=8}\). Note: the light gray zone in Figure 6 represents the heating cessation period.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Operation Case**} & **Heating Duration per** & **Hours Contained in a** \\  & **Operation \(\tau_{\text{o}}\) (h)** & **Heating Cycle \(\tau\) (h)** \\ \hline \(C_{\tau=0.5}\) & 0.5 h & 2.5 h \\ \(C_{\tau=1}\) & 1 h & 3 h \\ \(C_{\tau=2}\) & 2 h & 4 h \\ \(C_{\tau=4}\) & 4 h & 6 h \\ \(C_{\tau=8}\) & 8 h & 10 h \\ \hline \hline \end{tabular}
\end{table}
Table 3: Information of operation cases.  
approaching the indoor air temperature \(T_{\rm i}\) (18 \({}^{\circ}\)C to 20 \({}^{\circ}\)C). However, \(T_{\rm in,i}\) of the other three internal walls increases slowly and is obviously lower than the \(T_{\rm in,i}\) of Wall 4 during the whole heating period. Once the heating device is shut off, \(T_{\rm in,i}\) drops sharply for Wall 4, but drops slowly for the other three internal walls. The reason is the heat capacity of the inner layer of Wall 4 is the lowest, which leads to nearly no time lag between changes of \(T_{\rm in,i}\) and \(T_{\rm i}\) (indoor air temperature).  
Comparing Figure 6a,b, it can be seen that the \(T_{\rm in,i}\) of Wall 2 is equal to that of Wall 3 during heating period in Figure 6a. However, when it comes to the longer heating duration, as shown in Figure 6b, significant temperature difference is found between the inner surface of Wall 2 and Wall 3. This is because the thermal resistance of Wall 2 is smaller than Wall 3, which leads to more heat transferring to the inside of Wall 2 with the heating duration increases.  
The internal walls absorb and store heat from indoor air during the heating period. Then, some heat transfers through the internal walls, which leads to the fluctuation of surface temperature of internal walls close to the adjoining room. The outer surface temperature (\(T_{\rm in,o}\)) of internal walls close to the adjoining room is shown in Figure 7 for short and long heating duration.  
As shown in Figure 7a, the \(T_{\rm in,o}\) of four internal walls is similar to each other and close to the adjoining air temperature. It indicates that almost all the heat absorbed by the inner layer of internal walls is stored and little energy transfer to the outer surface of internal walls for short heating duration.  
An apparent increase of \(T_{\rm in,o}\) of four internal walls is found in Figure 7b for long heating duration, and the difference of \(T_{\rm in,o}\) between four walls increases with the increase of heating duration. The raise of \(T_{\rm in,o}\) ranks from high to low with the configuration of Wall 1, Wall 4, Wall 2, and Wall 3. This is dependent on the heat capacity of inner layer and thermal resistance of four internal walls. \(T_{\rm in,o}\) of the Wall 1 is the highest due to its higher thermal capacity and lower thermal resistance.