## 5 Results and Discussion
### Quantitative Description of the Local Heat Flux Variations
#### 5.3.2 Heat Flux Variations over Space (z Coordinate)  
As observed in Section 5.2, space variations of the wall-to-fluid heat flux are clearly noticeable in the adiabatic section of the present FPPHP, probably due to the conductive thermal interactions between the adiabatic section and the evaporator/condenser. To give a better insight into these local heat flux variations along space, _cvs_ was analyzed alike _cvt_. In Figure 14, _cvs\({}_{aw}\)_ and _cvs\({}_{std}\)_ are shown for the two considered orientations. Here, _cvs\({}_{aw}\)_ referring to both the vertical BHM orientation and the horizontal orientation decreases at low power inputs, to settle around 43% and 50%, respectively, at average-high power inputs. In addition, _cvs\({}_{std}\)_ decreases almost monotonically from a maximum of about 20% to a minimum of about 8% for both orientations. Such trends denote that the variations over space tend to gradually decrease during the intermittent flow regime in the overall device unlike time variations of Figure 13, while they stabilize during the full activation regime. Such a remark suggests that the conduction effects through the metallic section of the present FPPHP are evident in both orientations especially during the intermittent flow regime, where the unregular operation of each FPPHP branch promotes the onset of strong conduction along the z coordinate, as stated in [18]. On the other hand, the stabilization of _cvs\({}_{wt}\)_ at lower values during the full activation regime denotes less predominant conduction effects, confirming what was qualitatively observed in Section 5.2. Moreover, the higher values assumed by _cvs\({}_{aw}\)_ in the horizontal operation with respect to those assumed in the vertical BHM suggest that the wall-to-fluid interactions are distributed in a less uniform way along the z coordinate, probably due to weaker fluid oscillations. Finally, the values of _cvs_ in the present FPPHP assume much higher values with respect to those previously assessed for a tubular layout [46], where the conduction through the adiabatic section was almost negligible, thus confirming the presence of strong conductive phenomena occurring in the studied FPPHP geometry. Figure 13: _cvt\({}_{aw}\)_ and _cvt\({}_{std}\)_, as functions of the heat load, for the two considered orientations. To provide a reference for the understanding of conduction between the evaporator and the condenser at varying heat loads in the present FPPHP, the ratio between the power transferred only by conduction \(Q_{conduction}\) through the copper plate and the net power input given to the evaporator is shown in Figure 15. Specifically, using the values of evaporator and condenser temperature averaged over 5 min during the pseudo-steady state for each given heat load results in:  
\[Q_{conduction}=k(T_{eva}-T_{cond})\cdot S_{copper}/L_{adiab} \tag{29}\]  
where \(S_{copper}=T_{FPPHP}\cdot W_{FPPHP}-l_{channel}^{2}\cdot num\) is the full metallic cross-section of the device and \(L_{adiab}\) is the length of the adiabatic section. \(T_{FPPHP}\) is the device thickness, \(W_{FPPHP}\) is the device total width, \(l_{channel}\) is the side dimension of channels and \(num\) is the total number of channels. For both orientations, \(Q_{conduction}\) decreases with respect to the net power input, suggesting that more and more power provided to the evaporator is transferred by the working fluid to the condenser from the intermittent flow to the full activation regime. Hence, this confirms the reduction in terms of heat flux variations over space within the adiabatic  
Figure 14: \(cvs_{av}\) and \(cvs_{std}\), as functions of the heat load for the two considered orientations. Figure 15: Ratio between the power transferred by conduction between the evaporator and the condenser and the net power input to the evaporator as a function of power input for the horizontal orientation (**a**) and the vertical BHM (**b**).