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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on February 29, 2008
The Quarterly Journal of Mechanics and Applied Mathematics 2008 61(2):205-218; doi:10.1093/qjmam/hbn003
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Q. Jl Mech. Appl. Math, Vol. 61. No. 2 © The author 2008. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Free convective boundary-layer flow in a heat-generating porous medium: similarity solutions

J. H. Merkin{dagger}

( Department of Applied Mathematics University of Leeds, Leeds LS2 9JT )

{dagger} < amtjhm{at}maths.leeds.ac.uk>

Received 27 July 2007. Revise 17 December 2007. Accepted 17 December 2007.


  Abstract

The free convection boundary-layer flow on a vertical surface in a porous medium with local heat generation proportional to (T – T{infty})p, where T is the local temperature and T{infty} is the ambient temperature, is considered when there are power-law variations in either the wall temperature or the wall heat flux which enables the equations to be reduced to similarity form. When the wall temperature is prescribed, solutions are found for p ≤ 2 and p ≥ pc (pc = 10.673) with a saddle-node bifurcation at p = pc and two solution branches for p > pc. When the wall heat flux is prescribed, solutions are found only for p < 2. The special case p = 2 is considered and the limiting forms as p -> 2 and p -> {infty} are obtained and compared with the solutions obtained from solving the similarity equations numerically


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