The thermal impedance integral and the pathway decomposition of supercritical turbulent heat transfer. Part II. Experimental validation and scope of the linearised pathway form

In Part~I (\citealt{PartI}) the generalised Lyon integral was shown to become a thermal impedance when the pseudocritical barrier sweeps the boundary layer, and a two-point quadrature at the
barrier yielded the linearised pathway form LinP, $\mathrm{Nu}_b = \sqrt{\mathrm{Re}_b}\,\mathrm{Pr}_b^{-1/2} \allowbreak(\mathrm{Pr}_b/\mathrm{Pr}_w)^{1/4}$, with $w = 1/2$ derived from endpoint-swap invariance and $\beta = 1/2$ fixed from three classical correlation families. LinP is tested here in two stages against an experimental database spanning supercritical water at $23.5$--$24.5$\,MPa and CO$_2$ at $9$\,MPa, Reynolds numbers
$2.5 \times 10^4$ to $2 \times 10^6$, Prandtl numbers $0.8$ to $14$, and upward, downward and horizontal pipes. The first stage operates directly on the measured impedance. Across $2201$ measurement stations the wall-to-bulk impedance bias falls from $76\,\%$ for Dittus--Boelter to $6\,\%$ for the pathway form, and the effective pathway weight inverted from the measured impedance crosses $1/2$ at the bulk pseudocritical crossing for both fluids and all Reynolds numbers, a parameter-free confirmation of the symmetric weight. ... mehrThe second stage tests LinP predictively in the Q-mode against three comparators: the bulk-anchored entangled Bishop and the wall-anchored entangled Swenson correlations, each carrying a density ratio, and the uncorrected Dittus--Boelter. The penetration scaling $\mathrm{Nu}\sim\sqrt{\mathrm{Re}}$ is preferred over $\mathrm{Re}^{0.8}$ wherever the barrier is active. A wall/bulk role swap shows the spatial-mismatch pathology to follow whichever reference state traverses the pseudocritical temperature; the density ratio attenuates but does not cure it. Uncalibrated and density-uncorrected, LinP carries the lowest case-mean root-mean-square wall-temperature error, $31.5$\,K against $47.9$, $54.3$ and $55.1$\,K. Its residual deficits, confined to the deterioration peaks and the downflow regimes, trace to one missing ingredient: the pathway-resolved density correction beyond the linearised form.