## 5 Results and Discussion
### Link between Fluid Oscillations and Transverse Interactions  
During its operation, the thermal performance of a FPPHP might be significantly influenced by thermal interactions occurring between adjacent channels, which lead to a homogenization of temperature and, consequently, of the driven force for the working fluid  
Figure 16: Average dominant fluid oscillation frequency in the overall device **(a)** and channel-wise standard deviation **(b)** for the two considered FPPHP orientations. motion in the overall two-phase device [16; 50]. A local heat transfer analysis could thus be required to attempt a description of conduction between adjacent channels in FPPHPs. To this aim, the temperature distributions acquired by means of thermography, and properly regularized as thoroughly explained in [29], were adopted to provide an estimation of the heat flux exchanged between the \(n\)-th and \((n+1)\)-th channels by conduction \(q_{Fou,n\to n+1}\), according to [PERSON]'s law (along \(y\)-axis as defined in Figure 3):  
\[q_{Fou,n\to n+1}(z,t)=-k\frac{\partial T(y,z,t)}{\partial y} \tag{8}\]  
In particular, the partial derivative of \(T\) is evaluated in the median point between adjacent channels for every axial coordinate z as a function of time. The values averagely assumed by \(q_{Fou}\) over time were therefore adopted to estimate the power transferred by transverse conduction \(Q_{tr_{cond}}\) between every adjacent channel pair in the overall device along the adiabatic section (green box in Figure 1b) as follows:  
\[Q_{tr_{cond}}=\frac{\sum_{n=1}^{num-1}\left\{\left|\sum_{z=0}^{L_{ ratio}}mean[q_{Fou,n\to n+1}(z,t=1\dots N)\right|\cdot\Delta z\text{-}T_{FPPHP}] \right\}}{num-1} \tag{9}\]  
where \(num\) is the total number of FPPHP channels, mean is the arithmetic mean operator, \(N\) is the total number of time samples, \(L_{adiab}\) is the length of the adiabatic section framed by the IR camera, \(\Delta z\) is the distance between two consecutive pixels in the \(z\) direction of the thermographic data, and T_FPPHP is the device thickness. Finally, \(Q_{tr_{cond}}\) was normalized with respect to the net power input to the evaporator divided by the number of FPPHP channels, resulting in \(Q_{ratio}=Q_{tr_{cond}}/(\frac{Q}{num})\). Specifically, \(Q_{ratio}\) defines the percentage of transverse conduction with respect to the power potentially transferrable by a single FPPHP branch from the evaporator to the condenser. In Figure 17, \(Q_{ratio}\) is shown as a function of \(Q\) for both considered device orientations. For the vertical BHM, the effects of transverse conduction become more and more negligible as the power input to the evaporator increases. For the horizontal orientation, \(Q_{ratio}\) is almost equal to 15% at high power inputs, denoting instead strong conductive effects between adjacent channels in agreement with other literature findings [29; 30; 39; 51]. In fact, operating a FPPHP in horizontal orientation generally leads to a higher evaporator temperature due to lower thermal performances, eventually increasing the temperature of the fluid flowing towards the condenser. This may result in greater temperature gradients between adjacent branches, leading to higher thermal interactions between the working fluid and the side walls of the channels and, consequently, to stronger transverse interactions. Figure 17: \(Q_{ratio}\) as a function of the power input to the evaporator for both considered device orientations. The highlighted variation in terms of transverse conduction from vertical BHM to horizontal orientation may be due to different oscillatory and local heat transfer behaviors of the FPPHP, which are strictly linked to wall-to-fluid heat transfer interactions. To investigate the interplay between the local wall-to-fluid heat flux and transverse conduction \(q_{Fou,7\to 8}\), the heat flux \(q\) exchanged in two branches, i.e., channels 7 and 8, was compared with the corresponding heat flux \(q_{Fou,7\to 8}\) (\(z=0.02\) m) in terms of oscillation frequency.