## 5 Results and Discussion
### Quantitative Description of the Local Heat Flux Variations
#### 5.3.1 Heat Flux Variation over Time  
As already pointed out in Section 5.2, fluctuations over time of the local wall-to-fluid heat flux are able to describe the fluid oscillatory flow through the adiabatic section. Hence, the device performance, which is linked to its fluid dynamics, is believed to be strictly dependent on the local heat transfer interactions. To investigate such an interplay between global and local thermal behaviors, the values assumed by \(q\) over time in every FPPHP branch for a single axial coordinate, namely z = 0.02 m, were carefully investigated.  
In Figure 12, \(q\) is shown for two different operating conditions, i.e., horizontal orientation, \(Q\) = 50 W (Figure 12a), and vertical BHM orientation, \(Q\) = 150 W (Figure 12b); three representative channels are considered. In the horizontal configuration (Figure 12a), during the first 2 s of acquisition, the heat flux oscillates in every analyzed channel, suggesting fluid motion between the evaporator and the condenser, while it starts approaching null values after 2 s without any significant oscillation, denoting instead absence of fluid motion. On the contrary, in the vertical BHM operation (Figure 12b), \(q\) presents regular and persistent oscillations for every PHP branch, i.e., the fluid is regularly flowing in the overall adiabatic section.  
The heat flux variations over time were therefore statistically investigated by means of \(cvt\) to provide a quantitative description of fluid oscillations from intermittent flows to full activations. In Figure 13, \(cvt_{av}\) and \(cvt_{std}\) are shown for the two considered orientations as functions of the power input to the evaporator. For heat loads lower than 100 W, \(cvt_{av}\) reaches peaks of about 75%, while \(cvt_{std}\) decreases to about 10%. At average-high heat loads, \(cvt_{av}\) and \(cvt_{std}\) stabilize around 70% and 8% for both orientations, thus giving a further reference for the description of the significant change in slope of \(R_{eq}\) from intermittent flow to full activation of the device (Figure 7). The provided values and general trends of the statistical coefficients are in good agreement with those found in [46] for a tubular layout, although the very different geometry analyzed in the present work, suggesting the validity of the adopted statistical coefficients for other PHPs layouts.  
Furthermore, the intermittent flow regime in the horizontal orientation, when compared to the vertical BHM orientation, exhibits, at 50 W, higher values of \(cvt_{av}\) and \(cvt_{std}\). This suggests stronger variations over time of the heat flux from channel to channel and, consequently, a more intermittent operation of the FPPHP, in accordance with previous works [47; 48; 49]. Additionally, such evidence agrees with the higher value of equivalent thermal resistance observed in Figure 7. On the other hand, within the full activation of the system, \(cvt_{av}\) and \(cvt_{sdd}\) assume similar values for both orientations, highlighting comparable heat flux variations over time. Such similarity may explain the gradual approaching of equivalent thermal resistance referred to both orientations at elevated heat loads to the evaporator.  
Figure 12: Local heat fluxes referred to every channel for the horizontal orientation at \(Q\) = 50 W (**a**) and for the vertical BHM at \(Q\) = 150 W (**b**).