## 5 Results and Discussion
### Time Evolution of Fluid Oscillations
Both continuity and activity values shown in Tables 6 and 7 were therefore averaged over the entire device, i.e., for all channels, resulting in \(t_{c,av}\) and \(t_{a,av}\), respectively. In Figure 14, \(t_{c,av}\) is shown for both considered heat loads and device orientations. The vertical BHM exhibits lower values of \(t_{c,av}\) (around 23 and 27% of the total observation window), confirming the greater continuity of oscillations in the horizontal orientation, where \(t_{c,av}\) is equal to about 37 and 34% for average and high heat loads, respectively. However, a certain decrease in average continuity time with the increase in heat load is perceivable, denoting a reduction in fluid oscillation around the dominant frequency probably due to the onset of higher inertial forces, i.e., less stable oscillatory behavior [15; 16; 41]. \(t_{a,av}\) is instead shown  
Figure 13: Scalograms referred to channel 12 for the vertical BHM (**a**) and horizontal orientation (**b**), \(Q=250\) W; denoised scalograms (**c,d**) and frequency identification over time (**e,f**). in Figure 15 for the same test conditions. Here, the vertical BHM presents generally greater channel activity with respect to the horizontal orientation, since the gravity-assisted mode promotes the fluid motion in the overall device without significant stopovers, confirming what was observed in other works on FPPHPs, where the horizontal orientation usually results in a less stable operation of the device over time [22; 39; 42]. Additionally, for such an orientation, the activity time increases with the power input, while the horizontal mode presents similar activity times. This remark suggests that above a certain heat load, channel activity saturates in the horizontal orientation probably due to the absence of significant buoyancy forces. Higher activity times of the vertical BHM furthermore confirm the better thermal performance assessed in [29] for such an orientation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Channel**} & \multicolumn{4}{c}{**Q [W]**} \\ \cline{2-5}  & \multicolumn{2}{c}{**150**} & \multicolumn{2}{c}{**250**} \\ \cline{2-5}  & \(\mathbf{t_{c}}\) **[\%]** & \(\mathbf{t_{a}}\) **[\%]** & \(\mathbf{t_{c}}\) **[\%]** & \(\mathbf{t_{a}}\) **[\%]** \\ \hline
1 & _17.7_ & _52.1_ & _28.6_ & _89.9_ \\
2 & _14_ & _88.9_ & _30.5_ & _91.65_ \\
3 & _27.1_ & _88.1_ & _35.6_ & _73.7_ \\
4 & _24.2_ & _80.1_ & _43.4_ & _89.9_ \\
5 & _5.7_ & _47.1_ & _31.9_ & _79.9_ \\
6 & _34.3_ & _73.9_ & _13.3_ & _90.1_ \\
7 & _9.6_ & _65.1_ & _52.9_ & _85.7_ \\
8 & _11.6_ & _87.2_ & _25.1_ & _93.8_ \\
9 & _13.5_ & _74.4_ & _28.8_ & _92.7_ \\
10 & \(5\) & _49.7_ & _32.4_ & _99.7_ \\
11 & _69.5_ & _100_ & _15.5_ & _94.8_ \\
12 & _30.2_ & _81.8_ & _10.7_ & _86.6_ \\
13 & _36_ & _58.4_ & _8.7_ & _80.5_ \\
14 & _46.1_ & _80.3_ & _21_ & _99_ \\
15 & _12.5_ & _54_ & _31.4_ & _94.1_ \\
16 & _13.2_ & _46.8_ & _27.8_ & _84.7_ \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Continuity and activity evaluated for the vertical BHM. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Channel**} & \multicolumn{4}{c}{**_Q [W]**} \\ \cline{2-5}  & \multicolumn{2}{c}{**150**} & \multicolumn{2}{c}{**250**} \\ \cline{2-5}  & \(\mathbf{t_{c}}\) **[\%]** & \(\mathbf{t_{a}}\) **[\%]** & \(\mathbf{t_{c}}\) **[\%]** & \(\mathbf{t_{a}}\) **[\%]** \\ \hline
1 & _46_ & _46_ & _24.2_ & _38.3_ \\
2 & _16.9_ &