# Experimental and Theoretical Study on Operation Characteristics of an Oscillating Heat Pipe
## 4 Results and Discussion
### Thermal Resistance Correlation  
Figure 7 shows the modified thermal resistance curve. The modified conductivity curve is calculated by substituting Equation (14) into Equation (12). The thermal resistance curve is modified from the experimental data in Figure 6 by changing the heating input to the reciprocal of the heating input. It is observed that these two curves have a similar trend. It proves that the temperature variation influences the growth of the bubbles and the meniscus radium. This is consistent with that reported in the literature [5; 6; 26]. It proves that the assumption made for Equation (16), that the thermal resistance of the OHP mainly depends on the radial thermal conductivity and the other influencing factors, could be corrected by a correlation coefficient. Figure 8 shows the linear curve fitting using Equation (20), which is derived from Equation (16). The two constants \(\frac{e}{g}\) and \(C(k_{w},k_{a})\) are \(8.55\times 10^{-3}\) and \(-0.05\), respectively. Using the Root Mean Square (RMS) method in statistical analysis, the standard deviation for the difference in the thermal resistance between the curve fitting and the experimental data was 0.026. It is found that the proposed linear correlation could be used to reasonably predict thermal resistance. The error was mainly due to (i) thermal conductivity was based  
Figure 6: Thermal resistance of OHP under different heating powers. Figure 7: Modified radial thermal conductivity curve. on the two-dimensional hypothesis; (ii) thermal conductivity of copper and liquid was calculated from the average temperature, which could be improved using the varying temperature; and (iii) the relationship between heating input and the liquid film thickness was assumed to be linear, which could be improved using the real relationship obtained from visualization experimental study. Furthermore, as the heating power increases, local and periodical dry-out may occur, which may cause a sharp increase in temperature in the evaporator section and, hence, cause the heat transfer performance to deteriorate. Therefore, in this analysis, the heat input was limited to 100 W.  
Figure 9 shows the linear curve fitted with the experimental data reported in the literature [12]. It demonstrated that the proposed linear relation could be used to describe the performance characteristics of the OHP system under different filling ratios. As depicted in Figure 10, the two constants, \(\varepsilon/\varphi\) and \(C(k_{w},k_{a})\), varied with different filling ratios. This is consistent with that reported in the literature [12]. The filling ratio has a large effect on the OHP performance. As a result, the thermal resistance depends on the heating input and filling ratio. Figure 8: Linear fit of the total thermal resistance. Figure 9: Relationship between thermal resistance and heating input for an OHP system using deionized water as working fluid under different FRs based on Ref. [12]. Figure 11 demonstrated the application of the theory in the OHP system using Methanol as a working fluid. Once again, the results show that the proposed linear correlation could be used to present the relationship between the thermal resistance and heating input for this methanol OHP system. Compared to the water OHP system presented in Figure 9, the two constants \(\varepsilon/\varphi\) and \(C(k_{w},k_{a})\) were very different. Furthermore, the proposed linear correlation was also verified in OHP systems using Ethanol and Acetone as working fluids reported in the literature [12]. It was found that the linear correlation was also applicable to these working fluids. However, the two constant values change significantly for different working fluids as shown in Table 1. This could be explained by the equivalent thermal conductivity. Different working fluids have different thermal conductivity, which leads to a large change in the thermal conductivity in the liquid film and, hence, causes thermal resistance variation.