Heat transfer in porous media Rayleigh–Bénard convection at various Prandtl numbers

Abstract

We perform two-dimensional direct numerical simulations to study the effect of porous media on global transport properties and flow structures in Rayleigh–Bénard (RB) convection at different Prandtl numbers. The simulations are carried out in a square RB cell with uniformly placed circular obstacles, where the porosity spans between ϕ=1 and ϕ=0.75 with the Rayleigh number Ra fixed at 108, at two high Prandtl numbers (10,4.3) and two low Prandtl numbers (0.03,0.1). It is found that the Nusselt number Nu varies non-monotonically with decreasing porosity, first increased and then suppressed at both high-Pr and low-Pr cases, while the transition points are greatly advanced at low Pr. Though the trends are similar at low and high Pr, we point out that the physical mechanisms behind them are different. At high Pr, the porous media enhance the heat transfer by increasing the flow coherence at high porosity and inhibit the heat transfer by impeding the passage of the plume in the bulk region at low porosity. However, at low Pr, the viscous effect is weakened and the heat transfer is mainly through the large-scale circulation (LSC). As the porosity decreases, the LSC is enhanced and the flow is laminarized, inhibiting the shedding of the plume from the boundary layer. Moreover, we further explore the flow structure under the random distribution of obstacles and find some similarities in the evolution of the flow structure. The discovery of the new mechanism for porous media at low Pr advances the understanding of the effect of porous media on natural convection and may provide implications for industrial designs.