## 2 Measurement Method of Thermophysical Parameters for PCM in the Container
### DHFMA Method of PCM in the Container  
In the DHFMA method, the specimen is in thermal equilibrium at the beginning and the end of each temperature step. After considering the correction coefficient of the heat flux sensors, the integral of heat flow in each step can be calculated as the heat of absorption in each temperature step. Based on ASTM C1784, two heat flux sensors are used. When the temperature of the specimen changes from \(T_{a}\) to \(T_{b}\), the change of areal enthalpy \(h_{A}\) can be obtained by measuring the values of both heat flux sensors installed on the two plates, as shown in Equation (8). \[h_{A}(T_{a},T_{b})=\sum_{i=1}^{n}S_{up}\Big{(}E_{i-up}-E_{equil-up}\Big{)} \Delta\tau+\sum_{i=1}^{n}S_{down}\Big{(}E_{i-down}-E_{qui-down}\Big{)}\Delta\tau \tag{8}\]  
in which \(S\) is the sensitivity coefficient of the heat flux sensor after calibration, \(E\) represents the output voltage value of the heat flux sensor, and \(\Delta\tau\) is the time interval. \(E_{equil}\) represents the value of heat flow  
Figure 3: Schematic diagram of steady-state thermal resistance series structure. returning to the steady state after loading the temperature step. In theory, if the heating plates and the specimen are well insulated, the \(E_{equi}\) will be zero when the value of heat flow returns to the steady state. However, in the experiment, it was impossible to achieve complete insulation. As such, the \(E_{equi}\) was near zero but not equal to zero. At the same time, the subscript \(up\) represents the heating plate on the top, while the subscript \(down\) represents the heating plate on the bottom. Because the areal enthalpy of the heat flux sensor is not linear in the whole temperature range, the correction coefficient \(S_{HFM}\) (\(T_{a}\),\(T_{b}\)) needs to be calibrated. Then, the areal enthalpy of the specimen (\(h_{As}\) (\(T_{a}\),\(T_{b}\))) can be calculated in Equation (9), which contains the areal enthalpy of the container and the PCM. In addition, the volume specific heat within each temperature step is considered to be linear, so the volume specific heat of the specimen with the container at the average temperature (Equation (10)) is obtained, which is shown in Equation (11). \[h_{As}(T_{a},T_{b})=h_{A}(T_{a},T_{b})-\int_{T_{a}}^{T_{b}}S_{HFM}(T_{a},T_{b}) \text{d}T \tag{9}\]  
\[T_{mean}=\frac{1}{2}\times(T_{a}+T_{b}) \tag{10}\]  
\[C_{V}(T_{mean})=\frac{h_{As}(T_{a},T_{b})}{\delta\times(T_{b}-T_{a})} \tag{11}\]  
In order to obtain the heat of absorption of the PCM in the container, further calculation is needed. Since the volume of a PCM changes during the phase change, the specific heat of a PCM is expressed by mass specific heat. Firstly, the heat of absorption of full-scale specimen is expressed in Equation (12), and the heat of absorption of the container is calculated by Equation (13), where the volume specific heat of the container (\(C_{V\_box}\) (\(T\))) is measured by a HotDisk analyzer with an accuracy of 7%. \(V_{s}\) refers to the volume of the full-scale specimen, and \(V_{box}\) is the volume of the container's wall. Therefore, Equation (14) gives the mass specific heat of the PCM inside the full-scale container, in which \(m_{PCM}\) refers to the mass of the PCM. When a PCM is in the liquid or solid phase, \(C_{m\_PCM}\) refers to the sensible specific heat of a PCM. \[Q_{s}(T_{a},T_{b})=V_{s}\times\int_{T_{a}}^{T_{b}}C_{V}(T)\text{d}T \tag{12}\]  
\[Q_{box}(T_{a},T_{b})=V_{box}\times\int_{T_{a}}^{T_{b}}C_{V-box}(T)\text{d}T \tag{13}\]  
\[C_{m\_PCM}(T_{mean})=C_{m\_PCM}(T_{a},T_{b})=\frac{Q_{s}(T_{a},T_{b})-Q_{box }(T_{a},T_{b})}{m_{PCM}\times(T_{b}-T_{a})} \tag{14}\]  
In addition, the latent heat of the PCM inside the full-scale container needs to be calculated and compared with the DSC test result to verify the rationality of this method. Through the non-linear fitting of the test points of the solid and liquid phases, the fitting results can be used as the baseline in the phase transition interval.