Three-Dimensional Free Convection Boundary Layers in Porous Media Induced by a Heated Surface With Spanwise Temperature Variations

Abstract

In this paper we consider the effect of a nonuniform surface temperature distribution on the steady laminar free convection boundary layer flow induced by a vertical plate embedded in a fluid-saturated porous medium. The surface temperature profile exhibits sinusoidal variations in the spanwise (horizontal) direction, but the minimum temperature remains above or equal to that of the ambient medium. The resulting boundary layer flow is three-dimensional, and the governing equations are solved using a combination of a spanwise spectral decomposition and the Keller-box method. Detailed results in terms of the evolution of the rates of heat transfer and the developing thermal field are presented. The numerical work is supplemented by an asymptotic analysis valid far downstream where it is found that the effect of nonuniform heating becomes confined to a thin layer of uniform thickness embedded within the main growing boundary layer.