Free convective heat and mass transfer flow induced by an instantaneous point source in an infinite porous medium

A simple mathematical theory is proposed for the analysis of the buoyancy-driven heat and mass transfer flow induced by an instantaneous point source in an unbounded fluid-saturated porous medium of uniform porosity, assuming the validity of the Brinkman model. The theory consists of retaining only the leading terms of the series expansions of the dependent variables in terms of the thermal Rayleigh number and is valid within the limit of small Rayleigh numbers only. The heat generating rate is assumed to be not excessive, so that the induced flow is slow. The evolution of the flow field is demonstrated by drawing the streamlines at various times, and the results are delineated by comparing them with those of the Darcy flow model. The significance of the impact of species concentration gradients upon the thermally driven flow has been highlighted. Even though heat was specified to be one of the two diffusion mechanisms, the results apply as well to the case where the source simultaneously generates two different chemical components.