Numerical analysis of natural convection with conjugate heat transfer in coarse-grained porous media

Abstract

We report numerical simulations of fluid natural convection with conjugate heat transfer in a bottom-heated, top-cooled cubical cavity packed with relatively large (d/L=0.2) solid spheres in a Body Centred Tetragonal (BCT) configuration. We study largely varying solid-to-fluid thermal conductivity ratios between 0.3 and 198, for a fluid Prandtl number of 5.4 and fluid Rayleigh numbers between 1.16 × 10
⁶
and 1.16 × 10
⁸
and compare global heat transfer results from our present simulations to our previously published experimental results. The interplay between convection suppression due to the solid packing, and conductive heat transfer in the packing leads to three different regimes, each with a distinct impact of the solid packing on the flow and heat transfer. At low Rayleigh numbers ≈ 10
⁶
, all packings suppress convective flow. Compared to fluid only Rayleigh–Bénard convection, heat transfer is therefore reduced in low conductivity packings, whereas for high conductivity packings it is increased due to significant conductive heat transfer. At intermediate Rayleigh numbers ≈ 10
⁷
, low conductivity packings no longer suppress convection, whereas flow is still suppressed in high conductivity packings due to the thermal stratification imposed on the fluid by the solid. Consequently, heat transfer is lower compared to fluid only Rayleigh–Bénard convection, even in high conductivity packings. With a further increase of Rayleigh number ≳ 10
⁸
, convection starts to be the dominant heat transfer mechanism in all packings, and convective heat transfer is close to that for fluid only Rayleigh–Bénard convection. The contribution of solid conduction in high conductivity packings causes the overall heat transfer to be above that for Rayleigh–Bénard convectin.