Double Diffusion From a Heated Sphere in an Infinite Porous Medium

Abstract

Free convective heat and mass transfer from a sphere of constant temperature and concentration buried in an unbounded porous medium is studied analytically assuming the validity of the Darcy flow model. Using a regular perturbation analysis, transient and steady-state solutions have been obtained in the form of series expansions in terms of a thermal Rayleigh number, which is based on the temperature of the heated sphere and the medium permeability. The results are exemplified by drawing the streamlines at various times. Of special significance is the emergence of a downward flow in the transient state when the two buoyancy mechanisms are opposed. These results apply as well to the case of buoyancy-induced flows from a sphere generating simultaneously two different chemical components.