On convective boundary layer flows of a Bingham fluid in a porous medium

Abstract

In this short paper we consider the state-of-the-art with regard to convective boundary layer flows of yield-stress fluids in a porous medium. About a dozen papers have been published on the topic in the last 15years or so and each has presented a leading order boundary layer theory. For natural convection boundary layers of such fluids, the streamwise velocity field is confined to the boundary layer region but it is also delimited by a yield surface at which there is a precise balance between the yield stress and the buoyancy force. The aim of the present paper is to examine whether such boundary layer flows can exist in practice. We draw on a rigorous boundary layer theory formulated in terms of an asymptotically large Darcy–Rayleigh number, and attempt to determine how the fluid behaves in the region well outside of the boundary layer. We focus on the Cheng–Minkowycz problem, i.e. the free convective boundary layer flow which is induced by a uniformly hot semi-infinite vertical surface embedded in a porous medium.