Ultimate heat transfer in thermal convective turbulence between porous walls

Abstract

We have performed experiments of turbulent thermal convection in cylindrical container of aspect ratio D/H = 1, bounded by the two (heated or cooled) horizontal porous walls, where D and H are the diameter and the height of the container, respectively. The horizontal walls consist of porous media of the thickness L = H, in which there are many through-holes of diameter d ≈ 0.05H, connected with plenum chambers underneath and overhead. At the low Rayleigh number Ra ≲ 4 × 107, the Nusselt number Nu is comparable with that in turbulent Rayleigh−Bénard convection between impermeable (closed porous) walls, but as Ra increases, the wall permeability leads to significant heat transfer enhancement. At higher Ra ≳ 2 × 108, we have found the scaling Nu~Ra1/2 implying the ultimate heat transfer. The visualization of the temperature field using encapsulated the thermochromic liquid crystals has shown that strong large-scale thermal plumes, quite distinct from small-scale plumes observed in the non-porous case, appear in the ultimate state.