## 4 Results and Discussion
### Mechanisms of the Effect of Inclination Angle on Heat Pipe Performance
#### 4.4.1 Liquid Film Profile of the MF-AHPAs  
The heat pipe thermal performance is strongly affected by liquid film thickness. In the condensation section, an increase of the condensate thickness would lead to a degradation of heat transfer coefficient, and consequently a higher thermal resistance [51; 53]. In the evaporation section,  
Figure 10: Effect of inclination angle on thermal resistance of (**a**) acetone MF-AHPA; (**b**) cyclopentane MF-AHPA; and (**c**) n-hexane MF-AHPA. a higher height of liquid pool in evaporator hinders the formation of larger bubbles or film, as presented in the CFD result by [PERSON] et al. [51], which is unfavourable to the evaporation heat transfer rate, and hence heat pipe performance. Figure 11a-c present the effect of inclination angle on liquid film profile in the condensation section of the MF-AHPA with various working fluids at 90 W. The thickness of liquid film during condensation is developing from the side and growing as the condensate flows toward the evaporation section. As shown in Figure 11, the thickness of condensate decreases as the inclination angle increases, owing to the increasing influence of gravitational force. Due to the relatively smaller viscous friction factor (F\({}_{\text{I}}\)) and inertial vapour force factor (f\({}_{\text{inv}}\)), the acetone liquid film is shown to be thinner than those of the other two working fluids. 4.2 Relationship between Optimal Inclination Angle and Volumetric Fraction (\(\alpha_{\text{c,a}}\))  
There may be a relationship between the optimal inclination angle and volumetric fraction (\(\alpha_{\text{c,a}}\)). The optimal inclination angle can be determined by a minimum combined thermal resistance of evaporation and condensation processes. In fact, a universal optimal inclination angle does not exist. It varies with the working fluids, wicking structure, and heat loads. For example, at 90 W, the optimal inclination angle of the acetone heat pipe is 25\({}^{\circ}\), but it becomes 75\({}^{\circ}\) for both the n-hexane and cyclopentane heat pipes. In addition, the optimal inclination angle may be different in various  
Figure 11: Effect of inclination angle on the liquid film profile in the condensation section. (**a**) Acetone MF-AHPA; (**b**) cyclopentane MF-AHPA; and (**c**) n-hexane MF-AHPA. All of the heat pipes are at a heat load of 90 W.  
heat loads, even for the same heat pipe. For example, the optimal inclination angles of the acetone heat pipe with heat loads of 40 W, 90 W, 160 W, and 230 W are 10\({}^{\circ}\), 25\({}^{\circ}\), 45\({}^{\circ}\), and 75\({}^{\circ}\), respectively. In order to figure out the mechanism or criteria in determining an optimal inclination angle, the volumetric fraction, \(\alpha_{\rm c,a}\) (Equation (22)), which represents a fraction of working fluid in the section of condensation and adiabatic wick, is introduced. Figure 12 plots \(\alpha_{\rm c,a}\) as a function of the inclination angle. The effect of working fluid and heat load on the volume fraction \(\alpha_{\rm c,a}\) are shown in Figure 12a,b, respectively. Although the optimal angles vary significantly for heat pipes with different working fluids or heat loads, we observed that the corresponding volume fractions \(\alpha_{\rm c,a}\) show a very small variation, i.e., from 66.5% to 81.3%. Specifically, in Figure 12a, the \(\alpha_{\rm c,a}\) changes slightly from 66.5% to 70.8% when a large change of the optimal inclination angles with different working fluids, i.e., varying from 25\({}^{\circ}\) to 75\({}^{\circ}\). The same trend can be observed in Figure 12b for the acetone heat pipe at various heat loads. Experimental results clearly illustrate that the optimal inclination angle is strongly related to the liquid volumetric fraction \(\alpha_{\rm c,a}\). It appears that the mean value of the selected optimal volumetric fractions is 74%, with a fluctuation of \(\pm\)7%. The reason could be the dominance of the thermal resistance from the condensation section in grooved heat pipes.