Transient free convection with mass transfer on a vertical plate embedded in a h1gh-porosity medium

The problem of transient free convection is investigated in a high-porosity medium adjacent to a vertical semi-infinite flat plate with a simultaneous step change in wall temperature and wall concentration. The non-Darcian effects of convection, boundary, and inertia are all considered. The coupled nonlinear partial differential equations are solved by using a cubic spline collocation method. The numerical results show that the Darcy model overestimates both the transient heat and the mass transfer rate for a high-porosity medium. When the inertia effect is neglected, there is a minimum in the temporal transient Nusselt and Sherwood numbers before steady state is achieved. The present analysis also investigates the effects of the following parameters on the time required to reach steady state: buoyancy force ratio N, Darcy number Da, inertia coefficient T, and Lewis number Le. The time required to reach steady state decreases as or Da increases and increases as T increases. When Le < 1, the time decreases as Le increases, and for Le ≥ 1, the reverse is true.