## 4 Experimental Results
### Uncertainty Analysis  
Uncertainty analyses include the uncertainty analysis of the thermal conductivity measurement and the uncertainty analysis of the heat of absorption measurement. Based on Equations (1)-(7), the thermal resistance and thermal conductivity of the PCM in the container can be arranged as Equation (27) and Equation (28). Therefore, the uncertainty sources of the thermal conductivity measurement include uncertainties of temperature difference, thickness, heat flow, the thermal conductivity of the container measured by a HotDisk analyzer, and the contact thermal resistance calibration. \[R_{\text{PCM}}=R-R_{\text{ctr-down}}-R_{\text{ctr-up}}-R_{\text{box-down}}-R_ {\text{box-up}}=\frac{\Delta T}{q}-R_{\text{ctr}}-\frac{\delta_{\text{box}}}{ \lambda_{\text{box}}} \tag{28}\]  
\[\lambda_{\text{PCM}}=\frac{\delta_{\text{PCM}}}{R_{\text{PCM}}} \tag{29}\]  
Uncertainty analysis was performed using the thermal conductivity test data of erythiritol in a container with the heating temperature of 110 \({}^{\circ}\)C. Firstly, the temperature difference was calculated by the temperatures measured on the two plates. By considering the uncertainty of the temperature difference measurement and the acquisition error of data acquisition card [38], the standard uncertainty of temperature difference measurement was 0.11 \({}^{\circ}\)C. Then, the thickness of the container was measured by a vernier caliper, and the thermal expansion was also taken into consideration. The thermal expansion coefficient was measured by DIL 402C which is purchase from NETZSCH (Shanghai) Machinery and Instruments Co. Ltd. Branch Office Liaoning (Shenyang, Liaoning, China). As such, the standard uncertainty of the thickness measurement was \(9.69\times 10^{-6}\) m. Furthermore, the uncertainty of the heat flow measurement comes from the calibration process of the heat flux meter. Sources of calibration uncertainty include the uncertainty of thermal conductivity measured by a HotDisk analyzer, the uncertainty of the temperature difference measurement, and the uncertainty of the thickness measurement. The standard uncertainty of the heat flow measurement was 4.45 W/m\({}^{2}\). Similarly, the standard uncertainty of thermal contact resistance calibration was \(6.82\times 10^{-6}\) m\({}^{2.\circ}\)C/W. Figure 15: Sensible specific heat value of erythiritol. Equation (30) gives the uncertainty composition formula of PCM thermal resistance, and Equation (31) refers to the standard uncertainty of thermal conductivity of a PCM. \[u_{R_{PCM}}=\sqrt{\left(\frac{\partial R_{PCM}}{\partial\lambda T}\times u_{AT} \right)^{2}+\left(\frac{\partial R_{PCM}}{\partial q}\times u_{q}\right)^{2}+ \left(\frac{\partial R_{PCM}}{\partial q_{KP}}\times u_{R_{AP}}\right)^{2}+ \left(\frac{\partial R_{PCM}}{\partial q_{lux}}\times u_{Q_{lux}}\right)^{2}+ \left(\frac{\partial R_{PCM}}{\partial q_{lux}}\times u_{Q_{lux}}\right)^{2}} \tag{30}\]  
\[u_{A_{PCM}}=\sqrt{\left(\frac{\partial\lambda P_{PCM}}{\partial\delta\delta P_ {PCM}}\times u_{Q_{PCM}}\right)^{2}+\left(\frac{\partial\lambda P_{PCM}}{ \partial R_{PCM}}\times u_{R_{PCM}}\right)^{2}} \tag{31}\]  
Therefore, the standard uncertainty of the thermal conductivity measurement of erythritol was \(2.03\times 10^{-2}\) W/m-\({}^{\circ}\)C when the heating temperature was 110 \({}^{\circ}\)C, and the relative standard uncertainty was 3.27%. In this way, the uncertainty of the thermal conductivity measurement of n-docosane and erythritol in the container at different heating temperature can be obtained. The results show that the relative standard uncertainty was better than 3.79%. In addition, Equation (32) gives the calculate formula for heat of absorption of the PCM in the container, so the sources of uncertainty in the calculation of the heat of absorption can be obtained.