## 2 Materials and Methods
### Data Reduction and Uncertainty Calculation  
In general, both thermal resistance and threshold critical power are the key characteristics to evaluate the thermal performance of a heat pipe system. The threshold critical power means the highest operating power of a heat pipe before its inner working medium dries out. The thermal resistance of a heat pipe system is defined as the ratio of the temperature difference between the evaporation section and condensation section to the operating power. The total thermal resistance of two experimental heat pipe systems can be calculated as the following Equation (1):  
\[R_{\text{hp}}=\frac{\Delta T}{Q_{\text{in}}}=\frac{T_{\text{eva}}-T_{\text{ con}}}{Q_{\text{in}}} \tag{1}\]  
where \(T_{\text{eva}}\) and \(T_{\text{con}}\) are the average surface temperature of the evaporation section and condensation section, respectively. \(Q_{\text{in}}\) is the operating power during normal running. \(T_{\text{eva}}\) and \(T_{\text{con}}\) can be calculated as following Equations (2) and (3):  
\[T_{\text{eva}}=\frac{T_{1}+T_{2}}{2} \tag{2}\]  
\[T_{\text{con}}=\frac{T_{4}+T_{5}+T_{6}}{3} \tag{3}\]  
In this study, the experimental uncertainty was mainly caused by the accuracy of the instruments in the measurement process, including the accuracy of the wireless acquisition unit and DC power supply. The resolution of the DC power supply and wireless acquisition unit was 0.5 W and 0.05 \({}^{\circ}\)C. These measuring errors actually influenced the total thermal resistance of a heat pipe system according to Equation (1). The uncertainty of the thermal resistance could be calculated as following Equation (4) [28, 29, 30]:  
\[\begin{split}\frac{e(R_{\text{hp}})}{R_{\text{hp}}}& =\frac{\sqrt{\Big{(}\frac{2^{R_{\text{hp}}}}{4Q_{\text{in}}}{Q_{ \text{in}}}{Q_{\text{in}}}}^{2}+\Big{(}\frac{2^{R_{\text{hp}}}}{{aT_{1}}}{{r_ {1}}}\Big{)}^{2}+\Big{(}\frac{2^{R_{\text{hp}}}}{{aT_{2}}}{{r_{2}}}\Big{)}^{2 }+\Big{(}\frac{2^{R_{\text{hp}}}}{{aT_{4}}}{{r_{4}}}\Big{)}^{2}+\Big{(}\frac{2^ {R_{\text{hp}}}}{{aT_{5}}}{{r_{5}}}\Big{)}^{2}+\Big{(}\frac{2^{R_{\text{hp}}} }{{aT_{6}}}{{r_{6}}}\Big{)}^{2}}}{{R_{\text{hp}}}}\\ &=\frac{\sqrt{36\frac{\Delta T^{2}}{Q_{\text{in}}}^{2}{q_{\text{ in}}}^{2}+9{\sigma_{1}}^{2}+9{\sigma_{1}}^{2}+9{\sigma_{1}}^{2}+9{\sigma_{ 1}}^{2}+4{\sigma_{1}}^{2}+4{\sigma_{2}}^{2}+4{\sigma_{2}}^{2}}}}{Q_{\text{in}}{ R_{\text{hp}}}}\end{split} \tag{4}\]  
where \({\text{e}}{T_{1}}\), \({\text{e}}{T_{2}}\), \({\text{e}}{T_{3}}\), \({\text{e}}{T_{4}}\), \({\text{e}}{T_{5}}\), and \({\text{e}}{T_{6}}\) are the resolution of the wireless acquisition unit, which is 0.05 \({}^{\circ}\)C; \({\text{e}}{Q_{\text{in}}}\) is the resolution of DC power supply, which is 0.5 W. From Equation (4), it can be known that the uncertainty of the thermal resistance increases with the temperature difference between the evaporation section and condensation section (\(\Delta T\)) and decreases with the operating power (\(Q_{\text{in}}\)). Therefore, the maximum uncertainty of the total thermal resistance can be found when the temperature difference between the evaporation section and condensation section (\(\Delta T\)) is the biggest one, while the operating power (\(Q_{\text{in}}\)) is the  
Figure 2: Experimental setup of TSHP.  
smallest one. Therefore, in this study, the maximum uncertainty of the total thermal resistance was 8.2%.