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 plate 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 temperature 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 boundary layer evolves, a steady boundary layer is approached but far from the plate the ambient conditions remain. A complete analysis is made of the governing equations at t = 0, the steady state at large times and a series solution valid at small times is derived. A numerical solution of the full boundary-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 stream forces in the same direction) and negative (buoyancy and free stream forces in opposing directions). The uniqueness of this problem lies in the fact that we have been able to match significantly different profiles at the time when the forward integration approach breaks down and the solution at large times and establish a smooth evolution around the transition time. (C) 1998 Elsevier Science Ltd. All rights reserved.