On buoyancy induced heat and mass transfer from a concentrated source in an infinite porous medium

Abstract

This paper reports an analytical study of natural convection heat and mass transfer, induced by a concentrated source, located in an infinite porous medium. The transient and steady-state flow, temperature and concentration fields are obtained in terms of series expansions in the Rayleigh number based on the permeability of the porous medium and the heat generation rate from the source. The impact of the chemical species created by the source is to either aid or retard the flow induced by thermal buoyancy. Expressions determining the effect of species generation on the resulting transient and steady-state temperature and flow fields in the porous medium are reported in the course of the study. All discussions in this paper focus on the case where the net flow is upwards. Even though heat was specified to be one of the two diffusion mechanisms, the results of the present study apply as well to the case of buoyancy induced flow from a concentrated source generating simultaneously two different chemical components.