## 2 Methodology
### Sensitivity Analysis  
Several preliminary investigations were conducted to assess the influence of various parameters on the results.  
From a geometrical perspective, the primary unknown parameter is the channel height \(D\), which is determined by the placement of the HP surfaces during the domain generation. In practice, it is a result of the entire production process, spanning from initial assembly to the furnace exit, where the brazing material foil undergoes melting.  
For the first two matrix samples, a series of calculations was performed with the \(k-\epsilon\) realizable EWT turbulence model for specific Reynolds numbers, varying \(D\), as shown in Figure 7.  
On the horizontal axis, the variation \(\Delta D\) is presented relative to the reference that is \(D_{0}=2h\), with \(h\) being the nominal height of the dimples of the pressing-dieCAD models. The value of \(D\) corresponds to the set distance for the HPs, measured from the top to the bottom points of the dimples. On the vertical axis, the error, defined as the relative difference between the calculated \(\Delta P\) and experimental \(\Delta P_{exp}\) pressure drops, is reported.  
As observed, \(D\) significantly affects \(\Delta P\), as expected due to its relationship with the hydraulic diameter. The condition \(\Delta P=\Delta P_{exp}\) lies within a narrow range around \(D=D_{0}\).  
Taking these errors into account, and with the possibility to ensure a reliable, repeatable approach, all the geometries were therefore created with \(D=2h\).  
On the other hand, the effects on \(\Delta P\) of the matrix were due to the modifications of the brazed-feature diameters by \(\pm 10\%\) were negligible, fully covering the measured deviations. Nevertheless, for whole channels, this was not completely true for those near the ports, where higher velocities are experienced and maximum variations of up to \(\pm 2\%\) were noted.  
Figure 7: Dependence of numerical results on channel height for S1 and S2 matrices.  
To maintain consistency, and considering that such changes can typically arise during the manufacturing process, the brazed joints were modeled with a nearly constant thickness.  
A mesh sensitivity analysis was carried out to identify an appropriate element size, as presented for the entire channel of S1 in Figure 8, with the cell count expressed in millions. The focus on this sample is due to the fact that, along with S2, it represents a small-to-medium size BPHE in terms of plate area and capacity, ranging approximately from 20 to 300 kW. Therefore, a limit on the number of cells is necessary to enable calculations for larger devices while preventing unsustainable computational costs. An accuracy improvement of approximately 0.5% was obtained by doubling the cell count from 13.5 to 27 million, which is regarded as too high in light of the long-term perspective of conducting CHT simulations.  
Therefore, the settings used for generating the grid of S1 were chosen and scaled to the other geometries.  
Finally, varying the number of prismatic layers between 5 and 10 generally produced an increase in \(\Delta P\) of less than 1%. Larger values could not be achieved because of failures in volume mesh creation, which occurred where the walls are in close proximity and elements tend to collapse. That minimal impact is believed to be caused by continuous boundary-layer separations, as will be explained in the next section.