Unsteady mixed convection boundary-layer flow on a vertical surface in a porous medium

An analysis is made of the unsteady mixed convection from a vertical flat p late embedded in a fluid-saturated porous medium. For time t < 0 a uniform free stream velocity U exists parallel to the plate surface and the tempera ture T-infinity throughout the porous medium is uniform. Then at time t = 0 the temperature on the surface is instantaneously changed from the ambient fluid temperature T-infinity to T-w. At small times the transport effects are confined within a narrow layer adjacent to the plate. As this inner bou ndary layer evolves, a steady boundary layer is approached but far from the plate the ambient conditions remain. A complete analysis is made of the go verning equations at t = 0, the steady state at large times and a series so lution valid at small times is derived. A numerical solution of the full bo undary-layer equations is then obtained for the whole transient from t = 0 to the steady state. Results are presented to illustrate the occurrence of transients when the buoyancy parameter is positive (buoyancy and free strea m forces in the same direction) and negative (buoyancy and free stream forc es in opposing directions). The uniqueness of this problem lies in the fact that we have been able to match significantly different profiles at the ti me when the forward integration approach breaks down and the solution at la rge times and establish a smooth evolution around the transition time. (C) 1998 Elsevier Science Ltd. All rights reserved.