Periodic free convection from a vertical plate in a saturated porous medium, non-equilibrium model

The problem of the free convection from a vertical heated plate in a porous medium is investigated numerically in the present paper. The effect of the sinusoidal plate temperature oscillation on the free convection from the plate is studied using the non-equilibrium model, i.e., porous solid matrix and saturated fluid are not necessary to be at same temperature locally. Non-dimensionalization of the two-dimensional transient laminar boundary layer equations results in three parameters: (1) H, heat transfer coefficient parameter, (2) Kr, thermal conductivity ratio parameter, and (3) λ, thermal diffusivity ratio. Two additional parameters arise from the plate temperature oscillation condition which are the non-dimensional amplitude (ε) and frequency (Ω). The fully implicit finite difference method is used to solve the system of equations. The numerical results are presented for 0 ⩽ H ⩽ 10, 0 ⩽ Kr ⩽ 10, 0.001 ⩽ λ ⩽ 10 with the plate temperature oscillation parameters 0 ⩽ Ω ⩽ 10 and 0 ⩽ ε ⩽ 0.5. The results show that the thermal conductivity ratio parameter is the most important parameter. It is found also that increasing the amplitude and the frequency of the oscillating surface temperature will decrease the free convection heat transfer from the plate for any values of the other parameters.