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IMA Journal of Applied Mathematics Advance Access originally published online on November 13, 2007
IMA Journal of Applied Mathematics 2008 73(1):231-253; doi:10.1093/imamat/hxm048
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Free convection boundary layers on a vertical surface in a heat-generating porous medium

L. Mealey

J. H. Merkin{dagger}

Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK

{dagger} Email: amtjhm{at}maths.leeds.ac.uk

Received on January 26, 2007; Accepted on June 7, 2007

The natural convection boundary-layer flow on a solid vertical surface with heat generated within the boundary layer at a rate proportional to (T – T{infty})p (p ≥ 1) is considered. The surface is held at the ambient temperature T{infty} except near the leading edge where it is held at a temperature above ambient. The behaviour of the flow as it develops from the leading edge is examined and is seen to become independent of the initial heat input; however, it does depend strongly on the exponent p. For 1 ≤ p ≤ 2, the local heating eventually dominates at large distances and there is a convective flow driven by this mechanism. For p ≥ 4, the local heating does not have a significant effect, the fluid temperature remains relatively small throughout and the heat transfer dies out through a wall jet flow. For 2 < p < 4, the local heating has a significant effect at relatively small distances, with a thermal runaway developing at a finite distance along the surface.

Keywords: boundary layers; free convection; internal heat generation; Porous media.


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