Transient conjugate free convection due to a vertical plate in a porous medium

The problem of two-dimensional transient conjugate free convection due to a vertical plate of finite extent adjacent to a semi-infinite porous medium is investigated both analytically and numerically. In view of the number of nondimensional parameters present in the formulation, namely the Rayleigh number, Ra., the thermal conductivity and diffusivity ratios, k and α, respectively, between the plate and the porous medium, the heat capacity ratio, γ, for the porous medium and the plate aspect ratio, λ, a one-dimensional formulation is used to identify two parameter regimes, Ra ≫ 1 and Γ (= γα) ≪ Ra, and Γ ≫ 1 and Ra ≪ Γ, for which analytical solutions may be found; these are subsequently seen to compare favourably with computed solutions, also presented here, to the time-dependent governing heat and momentum equations. For the first of the parameter regimes mentioned above, the transient process is seen to develop towards the steady-state solution obtained by the same authors elsewhere.