Heat transfer and cross-diffusion due to a sphere of constant thermal energy embedded in a porous medium

Abstract

Heat transfer and cross-diffusion due to a sphere of constant thermal energy and concentration embedded in unbounded homogeneous porous medium in a regime where the temperature gradient produces mass flux is analytically studied using Darcy flow model. Analytical solution is obtained with regular perturbation analysis in the limit of small Rayleigh number. Due to cross-diffusion, solute front initially shows stronger convection than thermal front, but ultimately reaches steady-state at approximately the same time as that of thermal front. Quantity of heat necessary to maintain the steady-state is found to be least near the rear stagnation point and the mean Nusselt number is found to be unaffected by cross-diffusion. Nusselt number variation for different cone angles and Soret number is studied and it is found that higher improvement is achieved when cone angle is changed from 80 to 100°.