Thermo-diffusive Darcy flow induced by a concentrated source

An analytic study is made of Soret-induced double diffusive Darcy flow produced in an unbounded homogeneous porous medium of uniform porosity and low permeability when a concentrated source embedded instantaneously in the medium starts liberating heat and at the same time a chemical substance too at a constant rate in a regime where the temperature gradient produces mass flux as well. A perturbation analysis in the limit of small Rayleigh number is employed to obtain analytical solution for the determination of the transient and steady-state development of the flow field and heat and mass transfer. Due to double diffusion, a bifurcation of the flow field is noticed when the buoyancy mechanisms are opposed and due to the Soret-induced cross-diffusion, the region in which the thermal effect of the source is felt, gets minimized with a simultaneous reduction in the rate of momentum and heat transfer.