TRANSIENT FREE CONVECTION ABOUT A VERTICAL FLAT PLATE EMBEDDED IN A SATURATED POROUS MEDIUM

Abstract

An analysis is presented of the transient, buoyancy-induced flow and heat transfer in a Darcian fluid-saturated porous medium adjacent to a suddenly heated semi-infinite vertical wall. Transient profiles of the temperature field and the local Nusselt number are obtained by solving the unsteady boundary layer partial differential equations numerically. It is shown that the governing equations are of a singular parabolic type and can be solved accurately in a semi-similar, finite elliptic domain using a successive relaxation method. The solution thus obtained is compared with a solution obtained in the physical domain using an explicit upwind method. The results confirm that during the initial stage, before the effects of the leading edge are influential at a location, heat transfer and flow phenomena in porous media are governed by transient one-dimensional conduction. New data are presented for the transition from this initial conduction stage to a fully two-dimensional transient, which ultimately terminates in steady convection. It is also shown that in a Darcian medium the transient development of temperature field and local Nusselt number takes place monotonically, and unlike in homogeneous media, neither exhibits an overshoot.