Finite element analysis of heat transfer by natural convection in porous media in vertical enclosures

Abstract

Presents a numerical study on heat transfer by natural convection in porous media in vertical enclosures with side wall heating. The model for porous media includes inertia terms and also the Brinkman extension in addition to the Darcy resistance term. A semi‐implicit finite element scheme based on operator splitting method is adopted for solving the time‐dependent system of equations. The first half of the investigations is confined to the low permeability regime where Darcy law holds good. Presents the results for annular and rectangular cavities and proposes correlations for two types of boundary conditions, namely constant wall temperature case and uniform wall heat flux case. In the second half of the investigations, the scheme is applied in a high permeability regime, where the validity of Darcy law becomes questionable. Employs plane rectangular cavities with the two types of boundary conditions mentioned earlier. Highlights the influence of Rayleigh number ( Ra ) and Darcy number ( Da ) as separate parameters and proposes correlations for a square cavity for the first time in terms of Ra and Da as separate parameters. Discusses a qualitative study of the effect of aspect ratio on heat transfer as the permeability changes.