Vertical Free Convective Boundary-Layer Flow in a Porous Medium Using a Thermal Nonequilibrium Model

Abstract

In this article we study the effect of adopting a two-temperature model of microscopic heat transfer on the classical Cheng and Minkowycz (1977) vertical free convection boundary-layer flow in a porous medium. Such a model, which allows the solid and fluid phases not to be in local thermal equilibrium, is found to modify substantially the behavior of the flow relatively close to the leading edge, where the boundary layer is comprised of two distinct asymptotic regions. The numerical simulation of the developing boundary-layer relies heavily on near-leading-edge analysis to provide suitable boundary conditions. At increasing distances from the leading edge the difference between the temperatures of the fluid and solid phases decreases to zero, which corresponds to thermal equilibrium between the phases; this is confirmed by an asymptotic analysis.