The effect of a weak vertical magnetic field on the buoyancy-driven boundary-layer flow past a vertical heated wall

Abstract

In this paper we investigate the effect of a weak vertical magnetic field on the boundary-layer flow of an electrically conducting fluid past a vertical heated wall. We derive similarity solutions for the flow and temperature and show that the flow is composed of three regions: an inner region where the flow is a regular perturbation of the classical boundary-layer flow due to a heated semi-infinite vertical plate; an inviscid outer region where fluid is entrained from downwards towards the plate; and beyond this a quiescent region, separated from the outer region by a free shear layer. Thus the effect of the magnetic field is to inhibit the entrainment of fluid across the magnetic field lines in the whole region and confine it to an outer boundary layer.