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 buoya ncy-driven heat and mass transfer flow induced by an instantaneous poi nt source in an unbounded fluid-saturated porous medium of uniform por osity, assuming the validity of the Brinkman model. The theory consist s of retaining only the leading terms of the series expansions of the dependent variables in terms of the thermal Rayleigh number and is val id within the limit of small Rayleigh numbers only. The heat generatin g rate is assumed to be not excessive, so that the induced flow is slo w. The evolution of the flow field is demonstrated by drawing the stre amlines at various times, and the results are delineated by comparing them with those of the Darcy flow model. The significance of the impac t of species concentration gradients upon the thermally driven flow ha s been highlighted. Even though heat was specified to be one of the tw o diffusion mechanisms, the results apply as well to the case where th e source simultaneously generates two different chemical components.