Hydrothermal Convection in Saturated Porous Media

Convection in a porous cavity driven by heating in the horizontal is analysed by a number of different techniques which yield a fairly complete description of the two-dimensional solutions. The solutions are governed by two dimensionless parameters: the Darcy-Rayleigh number R and the cavity aspect ratio A. We first find solutions valid for shallow cavities, A → 0, by using matched asymptotic expansions. These solutions are given up to O(A6R4). For A fixed, we find regular expansions in R by semi-numerical techniques, up to O(R30) in some cases. Series-improvement techniques then enable us to cover the range 0 ≤ R ≤ ∞. A limited result regarding bifurcations is noted. Finally, for R → ∞ with A fixed, we propose a self-consistent boundary-layer theory which extends previous approximate work. The results obtained by these different methods of solution are in good agreement with each other and with experiments.

Convection in a porous cavity

Natural convection with combined heat and mass transfer buoyancy effects in a porous medium

On the boundary layer regime in a vertical enclosure filled with a porous medium

A numerical study of non-Darcian natural convection in a vertical enclosure filled with a porous medium is performed. The flow is modeled using the Brinkman-Forchheimer-extended Darcy equations. The governing equations are solved with the SIMPLER algorithm and good agreement with previously reported numerical and experimental results is found. An order of magnitude analysis and the numerical results demonstrate the importance of non-Darcian effects. For high Darcy numbers (Da > 10−4), both extensions are of the same order of magnitude and must be used simultaneously. In addition, Forch-heimer's extension must be included for Pr ≤ 1.0 and all Darcy numbers. Finally, Nusselt number correlations are presented for three different ranges of the Darcy number covering wide ranges of the governing parameters.

A numerical study of non-darcian natural convection in a vertical enclosure filled with a porous medium

This article describes the natural convective heat transfer in a vertical space insulated with a permeable material. A numerical solution to the problem is given for Ra0 ⩽ 200, which is the range of interest to building technological applications. The variables and boundary conditions and their influence upon the convective heat transfer are discussed. Comparisons are made with previously published results.

Claes G. Bankvall

Papers

Natural convection in vertical permeable space