## 3 Results and Discussions
### Thermal Performance  
To clarify the correlations among heating load, fluid flow motions and thermal performance of the OHPs and further reveal the corresponding fundamental effects of inner diameter, the variation in the overall thermal resistance \(R\) versus heating load under different inner diameters is presented in Figure 9, where \(R\) is defined as  
\[R=\left(\overline{T}_{\mathrm{e}}-\overline{T}_{\mathrm{c}}\right)/Q. \tag{5}\]  
In Equation (5), \(\overline{T}_{\mathrm{e}}\) is the average temperature of evaporator calculated as the mean temperature of \(T_{1}\)-\(T_{5}\) as shown in Figure 1b, and \(\overline{T}_{\mathrm{c}}\) is the average temperature of condenser computed by averaging the temperature values of all pixel points on the infrared thermal images of the condenser. In addition, in order to represent the effect of inner diameter on the thermal performance of the OHP, the dimensionless inner diameter of the OHP, \(D_{\mathrm{i}}\)*, is defined as  
\[D_{\mathrm{i}}^{*}=\frac{D_{\mathrm{i}}}{\sqrt{\sigma/g\Delta\rho}}=\frac{D_{ \mathrm{i}}}{\sqrt{\sigma/g(\rho_{\mathrm{i}}-\rho_{\mathrm{v}})}} \tag{6}\]  
where \(D_{\mathrm{i}}\) is the inner diameter of the OHP, \(g\) is the gravity acceleration, and \(\Delta\rho\) and \(\sigma\) are the difference of density between liquid and vapor and surface tension coefficient at (\(T_{\mathrm{e-r}}+T_{\mathrm{c-r}}\))/2, respectively. Herein, \(T_{\mathrm{e-r}}\) and \(T_{\mathrm{c-r}}\) are the reference temperatures of the evaporator and condenser, which are correspondingly defined as the highest operating temperature of the evaporator \(T_{\mathrm{e-r}}\) = 123.8 \({}^{\circ}\)C and ambient temperature of the condenser \(T_{\mathrm{c-r}}\) = 15 \({}^{\circ}\)C. Actually, \(D_{\mathrm{i}}\)* is another expression form of the Bond number, which can characterize the ratio between the surface tension and gravity. As indicated in Figure 9, under the small oscillation of working fluid, the heat exchanged between the hot and cold ends of the OHP mainly relies on the heat conduction of working fluid and tube body, resulting in a slight decrease of \(R\) with the increasing heating load. When the bulk oscillation of working fluid occurs, the heat and mass transfer in the OHPs are significantly improved, leading to the most apparent decrease in \(R\) versus the increasing heating load (e.g., the changing of \(R\) within \(Q\) = 60-120 W under \(D_{\mathrm{i}}\)* = 1.31 (\(D_{\mathrm{i}}\) = 2 mm) in Figure 9). After the appearance of working fluid circulation, the capabilities of heat and mass transfer in the OHPs are further enhanced to be a steady level due to a certain amount of filled working fluid, when the thermal resistance of the OHPs gradually drops to be a steady value (e.g., the changing of \(R\) within \(Q\) = 110-200 W under \(D_{\mathrm{i}}\)* = 1.31 (\(D_{\mathrm{i}}\) = 2 mm) in Figure 9). Note that the dry-out of working fluid will emerge in the evaporator, represented by the sudden growing-up of the thermal resistance (e.g., \(Q\) = 160 W under \(D_{\mathrm{i}}\)* = 0.65 (\(D_{\mathrm{i}}\) = 1 mm) and \(Q\) = 220 W under \(D_{\mathrm{i}}\)* = 1.99 (\(D_{\mathrm{i}}\) = 2 mm) in Figure 9). Herein, from the comparison among the changes of the thermal resistance and fluid flow motions versus heating load under different inner diameters of the OHPs, it can be seen that only the oscillation motions of working fluid occur in the major heating loads range (\(Q\)\(\leq\) 110 W) under \(D_{\mathrm{i}}\)* = 0.65 (\(D_{\mathrm{i}}\) = 1 mm), due to the large frictional flow resistance. Furthermore, even under the same mode of working fluid motions, the large frictional flow resistance under \(D_{\mathrm{i}}\)* = 0.65 (\(D_{\mathrm{i}}\) = 1 mm) also reduces the heat and mass transfer rate into the OHP. Therefore, the OHP with \(D_{\mathrm{i}}\)* = 0.65 (\(D_{\mathrm{i}}\) = 1 mm) has the highest thermal resistance relative to those under \(D_{\mathrm{i}}\)* = 1.31 (\(D_{\mathrm{i}}\) = 2 mm) and \(D_{\mathrm{i}}\)* = 1.99 (\(D_{\mathrm{i}}\) = 3 mm).