The effect of an embedded solid block on the onset of convection in a porous cavity

Abstract

Purpose – The purpose of this paper is to determine how the presence of an embedded, centrally placed, solid but heat-conducting block affects the onset and development of Darcy-Bénard convection. Design/methodology/approach – Steady solutions are obtained using finite difference methods with SOR as the smoother. A detailed presentation is given of how the interface conditions are modelled, and how a continuity of pressure argument is used to determine the value of the streamfunction on the solid block. Findings – The presence of the block affects strongly both the onset of convection and the nonlinear properties such as the mean Nusselt number and the strength of the fluid circulation. The smallest possible critical Darcy-Rayleigh is found to be 22.0152, which is smaller than 4π2, the value when the block is absent. Research limitations/implications – The Darcy-Rayleigh number is restricted to values at or below 200, which is five times the critical value without a solid block, but the size and conductivity of the block vary between all admissible values. Originality/value – This is the first investigation of the effect of internal obstacles on Darcy-Bénard convection.