Natural convection from point source embedded in Darcian porous medium

Abstract

The buoyancy induced convection arising from a point heat source in a fluid saturated Darcy porous medium bounded by an adiabatic conical surface, of apex angle 2θω, has been studied. The point heat source is located at the apex and the axis of the conical surface coincides with the direction of bouyant force vector. The self-similar equations are obtained for 0 < θω < π and Rayleigh number Ra from zero to infinity. The numerical solutions of self-similar equations have been obtained for θω (free plume), 3π/4, π/2 (plume bounded by horizontal surface), and π/4. It is shown that for a given Ra, the centre line velocity and temperature increases as πω (the bounding space) decreases. A perturbation solution for Ra → 0 also been studied to present closed form solution.