Transient non-Darcy forced convective heat transfer from a flat plate embedded in a fluid-saturated porous medium

Abstract

Transient non-Darcy forced convection on a flat plate embedded in a porous medium is investigated using the Forchheimer-extended Darcy law. A sudden uniform pressure gradient is applied along the flat plate, and at the same time, its wall temperature is suddenly raised to a high temperature. Both the momentum and energy equations are solved by retaining the unsteady terms. An exact velocity solution is obtained and substituted into the energy equation, which then is solved by means of a quasi-similarity transformation. The temperature field can be divided into the one-dimensional transient (downstream) region and the quasi-steady-state (upstream) region. Thus the transient local heat transfer coefficient can be described by connecting the quasi-steady-state solution and the one-dimensional transient solution. The non-Darcy porous inertia works to decrease the velocity level and the time required for reaching the steady-state velocity level. The porous-medium inertia delays covering of the plate by the steady-state thermal boundary layer. © 1990.