Double diffusive Darcy flow induced by a spherical source

A simple mathematical theory is proposed for the study of the free convective mass transfer flow induced by a spherical source in an unbounded porous medium assuming the validity of the Darcy flow model. Besides generating heat, the source generates a chemical substance too at a constant rate. Assuming the heat generation rate not excessive, an exact analytical solution is obtained for the flow field using the method of superposition for the determination of the temperature and concentration fields. The significance of the impact of the species concentration gradients upon the thermally driven flow has been highlighted. The results are delineated by comparing them with those of a point source and the evolution of the flow field is contrasted with that due to the presence of a heated sphere. Solutions for sources with spherical geometry could be deduced algebraically from the results of this study.