Transient free convection with mass transfer from an isothermal vertical flat plate embededded in a porous medium

Abstract

The problem of transient free convection in a porous medium adjacent to a vertical semi-infinite flat plate with a simultaneous step change in wall temperature and wall concentration is investigated. Nondimensionalization of the transient boundary-layer equations results in three governing parameters: (1) Le, the Lewis number, (2) N, the bouyancy ratio, and (3) ε, the value of the porosity of the porous medium divided by the ratio of heat capacity of the saturated porous medium to that of the fluid. The resulting nonlinear partial differential equations are solved by an explicit finite-difference method. The numerical results are presented for 0.3≤Le≤100, 0≤ N≤10 and for ε = 0.5, 1, and 2. It is shown that for a given Le and ε the time required to reach the steady state decreases as N increases; for a given N and ε, when Le<1, the time decreases as Le increases, while for Le ≥ 1, the reverse trend is true; and for a given N and Le, the time increases as ε increases. The final steady-state profiles are in good agreement with similarity solutions. Moreover, a simple relation of predicting the length of time for which a one-dimensional heat/mass transport will exist is obtained.