## 3 Calibration  
### Calibration Method of Contact Thermal Resistance  
Contact thermal resistance is mainly affected by surface geometry, pressure load, temperature, and contact material. In the calibration process, factors other than temperature should be avoided as far as possible. In this paper, 304L stainless steel was used as the calibration material of contact thermal resistance. The geometrical morphology of the material is represented by its surface roughness, so the 304L stainless steel with the same surface processing type as the full-scale container was selected to reduce the influence of roughness. In addition, the contact material is always an SiC plate and 304L stainless steel, so this factor can be ignored. Therefore, the function relationship between temperature and contact thermal resistance needs to be calibrated under the same pressure loaded on the specimen. In order to obtain the temperature gradient across the 304L stainless steel, three thermocouples sheathed with stainless steel of 2 mm in diameter, were placed in the holes drilled to the center of the specimen at distances of 10 mm, 25 mm, and 40 mm from the heating plate. The locations of the thermocouples are shown in Figure 4.  
In a previous study [27], the sensitivities of both heat flux sensors installed on the plates were calibrated with varying temperatures, as shown in Equation (16) and Equation (17). Thus, the heat flux across the calibration material can be calculated by Equation (18), in which \(E_{1}\) and \(E_{2}\) represent the output voltage of two heat flux sensors, respectively. \[S_{down}(T_{down})=2.82\times 10^{-3}\times T_{down}+48.25 \tag{16}\]  
\[S_{up}(T_{up})=2.59\times 10^{-3}\times T_{up}+48.93 \tag{17}\]  
\[q=\frac{S_{up}\big{(}T_{up}\big{)}\times E_{up}+S_{down}(T_{down})\times E_{ down}}{2} \tag{18}\]  
The measurement results for when the heating temperature was 100 \({}^{\circ}\)C are shown in Figure 5; here, Figure 5a gives the two heat flux testing results, and Figure 5b shows the linearity of the temperature gradient in the material. According to the least square method, the temperature value of the hot end (\(T_{H}\)) was 89.3 \({}^{\circ}\)C, while the cold end (\(T_{C}\)) of the calibration material was 87.1 \({}^{\circ}\)C. The average heat flux across the specimen was 672.03 W/m\({}^{2}\), which was calculated by Equation (18). Figure 4: The location of the thermocouples in the specimen. Therefore, the contact thermal resistances of both plates are expressed by Equation (19) and Equation (20). \[R_{ctr-down}(T_{down})=\frac{T_{down}-T_{H}}{q} \tag{19}\]  
\[R_{ctr-up}(T_{up})=\frac{T_{C}-T_{up}}{q} \tag{20}\]  
In order to study the relationship between contact thermal resistance and temperature (as well as for future research), the setting temperature range of the calibration experiment was from 100 to 900 \({}^{\circ}\)C for every 100 \({}^{\circ}\)C, and the values of contact thermal resistance at other temperatures were deduced. Figure 6 shows the calibration results of contact thermal resistance at different heating temperatures. It can be seen that there were non-linear exponential relationships between the contact thermal resistances of both plates and temperature. With the increase of temperature, the contact thermal resistance between the two plates and the calibration material decreased gradually. Due to the expansion of the calibration material, the actual contact area between the two plates increased. The contact thermal resistance fitting results of both plates are shown in Equation (21) and Equation (22). \[R_{ctr-down}(T_{down})=0.00334+0.01722\times e^{-\frac{T_{down}}{325.68973}} \tag{21}\]  
\[R_{ctr-up}(T_{up})=0.00392+0.01776\times e^{-\frac{T_{up}}{325.30734}} \tag{22}\]  
Therefore, during the experimental test, the contact thermal resistance between the PCM specimen in a container and the plates could be estimated approximately under the same pressure by using Equation (21) and Equation (22).