## 2 Design, Working Fluid, and Experimental Apparatus of the MF-AHPA
### Working Fluids Selection and Evaluation
#### 2.2.2 Evaluation of the Working Fluids  
A group of parameters that could help understand the effect of working fluid properties on heat pipes were calculated including flowing viscous friction (F\({}_{\rm I}\)), inertial vapour force factor (f\({}_{\rm inv}\)), Bond number (Bo), Galilei number (Ga), and Laplace number (La), as shown in Table 3. The definitions and formulae of each parameter are detailed as follows.  
The flowing viscous friction of the working fluid in the grooves by transferring unit power (F\({}_{\rm I}\)) [44] is defined as:  
\[F_{\rm I}=\frac{\mu_{\rm I}}{\rm KA_{w}\rho_{\rm I}h_{fg}} \tag{2}\]  
where \(\mu_{\rm I}\) is the dynamic viscosity of the liquid, K is the permeability, \(\rm A_{w}\) is the wick cross-sectional area, \(\rho_{\rm I}\) is the liquid density, and \(h_{\rm fg}\) is the latent heat of vaporisation.  
The vapour exerts a shear force at the interface between the vapour and the wick surface. This action would entrain droplets back into the condensation section. The inertial vapour force factor (f\({}_{\rm inv}\)) represents the magnitude of inertial vapour force produced by the properties of working fluid. It is defined as [44]:  
\[f_{\rm inv}=\frac{1}{\rho_{\rm v}h_{\rm fg}^{2}} \tag{3}\]  
The Bond number is defined as the ratio of gravitational forces and surface tension force. A low Bond number indicates that surface tension effect dominates [45]. It is calculated by:  
\[\rm Bo=\frac{r_{\rm hh}^{2}g(\rho_{\rm I}-\rho_{\rm v})}{\sigma} \tag{4}\]  
where \(r_{\rm hh}\) is the hydraulic radius of the groove.  
The Galilei number presents the ratio of gravitational forces and viscous force, which is expressed by:  
\[\rm Ga=\frac{gr_{\rm hh}^{3}\rho_{\rm I}^{2}}{\mu_{\rm I}^{2}} \tag{5}\]  
The Laplace number is the ratio of surface tension and momentum diffusivity, which is calculated by:\[\text{La}=\frac{\sigma\rho_{\text{I}}\text{Th}_{\text{I}}}{\mu_{\text{I}}^{2}} \tag{6}\]  
The calculated parameters of working fluids are closely related to the heat pipe performance. The Ga number presents the flowing capacity of working fluid driven by gravity only. The inertial vapour force factor (f\({}_{\text{inv}}\)) reflects the flow friction of working fluid vapour in the vapour channel. As shown in Table 3, acetone is supposed to have the smallest liquid-vapour shearing force due to the smallest f\({}_{\text{inv}}\) value of 1.57 \(\times\) 10\({}^{-12}\) m\({}^{3}\)kg/J\({}^{2}\). The liquid spreading that is driven only by capillary pressure could be evaluated by the La number. The viscous friction (F\({}_{\text{I}}\)) reflects the flow resistance in wicks for a given heat load. The working fluid with a smaller F\({}_{\text{I}}\) corresponds to a larger heat transfer limitation [46]. In addition, as reported by [PERSON] et al. [27], a working fluid with a low La number correlates to a lower heat transfer capacity. A liquid with a large La number may have better local temperature uniformity if a capillary wick is applied. Thus, acetone, with the smallest F\({}_{\text{I}}\) (230 N\(\cdot\)s/m\({}^{3}\cdot\)J), f\({}_{\text{inv}}\) (1.57 \(\times\) 10\({}^{-12}\) m\({}^{3}\)kg/J\({}^{2}\)) and largest Ga (621.2) and La (50,205), is supposed to have a relatively higher heat transfer capacity, better drainage of condensation liquid, and local temperature uniformity.