## 5 Results and Discussion  
### Global Performance Evaluation  
The device was first characterized, for every considered study case, by evaluating its global performance, which is the most employed figure of merit in the description of PHPs [3]. Hence, the equivalent thermal resistance was quantified by means of the following definition:  
\[R_{eq}=\frac{T_{eva}-T_{cond}}{Q_{net}} \tag{23}\]  
where \(T_{eva}\) and \(T_{cond}\) are the evaporator and condenser temperatures, respectively, averaged over 5 min during the pseudo-steady state of the FPPHP, and \(Q_{net}\) is the net power input provided to the evaporator. Since part of the evaporator section was not insulated, \(Q_{net}\) was quantified as \(Q_{net}=Q-Q_{diss}\), where \(Q_{diss}=S^{\prime}_{eva}\)-\(h_{env}(T_{eva}-T_{env})\) is the power dissipated at the evaporator section to the environment by free convection and radiation. The non-insulated evaporator surface \(S^{\prime}_{eva}\) was estimated, according to the FPPHP geometry, equal to 0.0037 m\({}^{2}\). The maximum dissipated power of about 1.4 W was found for the most critical case in terms of device operation, such as the horizontal orientation, \(Q=250\) W, where the evaporator exhibited an average temperature of 50 \({}^{\circ}\)C. During the tests, the environmental temperature \(T_{env}\) ranged from about 18 \({}^{\circ}\)C to 21 \({}^{\circ}\)C.  
Moreover, the uncertainty \(\delta_{R_{eq}}\), referred to each value of \(R_{eq}\), was evaluated by means of the approach by [PERSON] and [PERSON] [45]:  
\[\delta_{R_{eq}}=\sqrt{\left(\frac{1}{Q_{net}}\delta_{\Delta T}\right)^{2}+ \left(-\frac{\Delta T}{Q_{net}{}^{2}}\delta_{Q_{net}}\right)^{2}} \tag{24}\]  
where \(\delta_{\Delta T}\) is the uncertainty referring to \(\Delta T=(T_{eva}-T_{cond})\) and \(\delta_{Q_{net}}\) is the uncertainty on the net heat load, which depends on the uncertainty of the power supply (Table 1). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(E\) [\%] & \multicolumn{3}{c}{\(f\) [Hz]} & \(\sigma\) [K] \\ \hline
**Amp [W/m\({}^{2}\)]** & _0.5_ & _0.8_ & _1.2_ & \\ \hline
2000 & 11.30 & 11.53 & 12.44 & \\
4000 & 10.92 & 11.41 & 12.66 & _0.01_ \\
8000 & 10.77 & 11.60 & 13.13 & \\ \hline
2000 & 14.30 & 14.33 & 14.48 & \\
4000 & 12.16 & 12.06 & 12.56 &In Figure 7, the resulting \(R_{eq}\) evaluated by means of Equation (23) is shown for each net heat load and configuration, together with the corresponding error bars. The equivalent thermal resistance for the empty device was assessed to be almost equal to 0.7 K/W. In particular, the empty device was tested by adopting the same experimental set-up described in Section 2 (although the device was not here filled with working fluid after the vacuuming procedure). In fact, comparing the thermal performance of the partially filled device with the empty one through the same experimental apparatus is a rather standard procedure in the PHP field, which discloses the thermal advantages of using a certain amount of working fluid for a given PHP geometry [3; 11; 18]. Heat loads of 50, 100 and 150 W were, respectively, provided to the evaporator. As expected, the equivalent thermal resistance of the empty device (filling ratio = 0%) was higher than that of the device partially filled with fluid (filling ratio = 50%). Moreover, \(R_{eq}\) did not change from heat load to heat load, since heat transfer between the evaporator and the condenser was here solely due to conduction through the metallic walls. It has to be pointed out that \"low heat loads\" and \"average-high heat loads\" in Figure 7 are expressions whose meaningfulness is only related to the operational limits of the device under investigation. The maximum power input of 250 W was set as safety threshold for the experimental equipment, even though the device could have endured even higher power inputs before the onset of a full dry-out at the evaporator section (i.e., before the FPPHP failure).