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IMA Journal of Applied Mathematics Advance Access originally published online on November 21, 2007
IMA Journal of Applied Mathematics 2008 73(2):345-360; doi:10.1093/imamat/hxm037
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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.

Transient diffusion-controlled smoulder propagation: a similarity solution approach

J. Adler{dagger} and D. M. Herbert

Mathematics Department, Imperial College London, London SW7 2AZ, UK

{dagger} Email: mejadler{at}aol.com

Received on December 5, 2005; Accepted on May 17, 2007

One-, two- and three-dimensional time-dependent smoulder propagation through solid reactants with plane bounding surfaces is considered. Propagation is maintained by the diffusion of oxidizer from the boundaries to the smouldering reaction zone. The resulting burnt solid is assumed to be porous and the unreacted solid is taken to be sufficiently dense for no oxidizer to be present. The activation energy of the reaction is taken to be so large that the exothermic reaction term has a delta-function behaviour. This enables the reaction zone to be approximated by a narrow reaction front and results in the equations of heat and mass transfer being decoupled away from the front. The assumption, based on experimental observations, that the reaction fronts propagate with a speed proportional to t–1/2, where t is the time, permits the introduction of similarity variables. The resulting intermediate asymptotic equations, lying between those for very small and very large times, are solved and the equation of the smouldering fronts determined for each geometry is considered.

Keywords: smouldering combustion; diffusion controlled; time dependent.


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