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

Direct numerical simulation (DNS) results of porous-wall turbulent flows in open channels with conjugate heat transfer are reported. For the conductive porous walls considered, the change in heat transfer is non-monotonic with permeability. The heat flux initially decreases when going from a conductive smooth wall to slightly porous walls. In this initial regime, the near-wall flow remains smooth-wall like and the heat transfer in the porous wall is dominated by molecular diffusion. A reduction of the more favourably conducting solid material then diminishes the heat transfer, whereas the skin friction monotonically increases with permeability. Beyond a certain permeability the near-wall flow transitions to the Kelvin–Helmholtz (K–H)-like regime (Gómez-de Segura & García-Mayoral 2019 J. Fluid Mech. 875, 124–172; Habibi Khorasani et al. 2024 J. Fluid Mech . 984, A63) with cross-stream rollers. The heat flux increases with permeability and eventually surpasses that of smooth-wall turbulence. Once in the K–H-like regime, turbulent heat transport can deeply penetrate the porous wall and be comparable to the turbulent heat transport in the channel region. Thermal performance is assessed in terms of the Reynolds analogy breakdown, which is the disparity between the fractional increases in the Stanton number, italic St St St , and the fractional increases in the skin-friction coefficient, upper C Subscript f C f C-1pt f , relative to smooth-wall flow (Bunker 2013 Proceedings of the ASME Turbo Expo 2013 ; Rouhi et al. 2022 J. Fluid Mech . 951, A45). Similar to rough walls, the breakdown is unfavourable for porous walls, which is due to growing dissimilarities between the transfer of momentum and heat near the porous wall as it becomes more permeable. Turbulent sweep and ejection events contribute more to momentum transfer than to heat transfer. However, unlike for rough walls, a saturation limit for heat transfer is not observed.