Transient free convection about a vertical flat plate embedded in a porous medium

Abstract

The problems of transient free convection in a porous medium adjacent to a vertical semi-infinite flat plate with a step increase in wall temperature and surface heat flux are considered in this paper. By assuming a temperature profile in each case, the governing equation for the boundary layer thickness is obtained by an integral method. These governing equations are first-order partial differential equations of the hyperbolic type that can be solved exactly by the method of characteristics and approximately by the method of integral relations. The results based on the method of characteristics clearly indicate that during the initial stage when the leading edge effect is not being felt, heat is transferred as if by transient 1-dimensional heat conduction. At a later time, depending on the vertical location, the heat transfer characteristics change from transient 1-dimensional heat conduction to steady 2-dimensional convection. The thickness of the boundary layer is shown to be increasing with time until it reaches steady state where its value remains constant thereafter. The growth rate of the boundary layer thickness exhibits a discontinuity at the end of the transient period and the beginning of the steady state period. On the other hand, the results based on the method of integral relations show that the boundary layer thickness grows continuously with time and approaches the steady state value asymptotically; the growth rate of the boundary layer thickness decreases from a finite value to zero continuously as the steady state is approached. Except between the end of the transient period and the beginning of the steady state period, the results based on the method of integral relations are in good agreement with those based on the method of characteristics.