Turbulent heat transfer in open-channel flows with a thermally-conductive porous wall

Results of direct numerical simulations (DNS) of porous-wall turbulent flows in open channels with conjugate heat transfer are reported in this work. For the conductive porous walls considered here, the change in heat transfer is not monotonic. The heat flux initially decreases when going from a conductive smooth wall to slightly porous walls. In this initial porous-wall turbulence regime, the near-wall flow remains smooth-wall like and the heat transfer is dominated by molecular diffusion. As such, a reduction of the more favorably conducting solid material diminishes the overall heat transfer performance. Beyond a certain level of permeability however, the near-wall flow transitions to the K-H-like regime marked by the presence of cross-stream rollers, and the heat flux undergoes an increasing trend until it eventually surpasses that of smooth-wall turbulence. Neglecting the thermal behavior of the solid material can therefore result in overestimation of any gains in heat transfer. Additionally, thermal performance is assessed in terms of the Reynolds analogy breakdown, which is the disparity between the fractional increases in the Stanton number, $St$, and the fractional increases in the skin-friction coefficient, $C_f$, relative to smooth-wall flow. Similar to rough walls, the breakdown is unfavorable for porous walls. The unfavorable breakdown in Reynolds analogy is due to growing dissimilarities between the transfer of momentum and heat in the vicinity of the porous wall as it becomes more permeable. Turbulent sweep and ejection type events contribute more significantly to momentum transfer across the permeable surface than they do to heat transfer. However, unlike for rough walls, a saturation limit for heat transfer is not observed for the porous walls considered here. How much of a maximum increase in heat transfer can be achieved is something that remains to be determined.