The effects of heat exchange and fluid production on the ignition of a porous solid

Shah, A.A., Brindley, J., McIntosh, A. and Rademacher, J. (2008) The effects of heat exchange and fluid production on the ignition of a porous solid. Nonlinear Analysis: Real World Applications, 9, (2), 562-584. (doi:10.1016/j.nonrwa.2006.12.002).


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In this paper we study a system of nonlinear parabolic equations representing the evolution of small perturbations in a model
describing the combustion of a porous solid. The novelty of this system rests on allowing the fluid and solid phases to assume different temperatures, as opposed to the well-studied single-temperature model in which heat is assumed to be exchanged at an
infinitely rapid rate. Moreover, the underlying model incorporates fluid creation, as a result of reaction, and this property is inherited by the perturbation system. With respect to important physico-chemical parameters we look for global and blowing-up solutions,
both with and without heat loss and fluid production. In this context, blowup can be identified with thermal runaway, from which
ignition of the porous solid is inferred (a self-sustaining combustion wave is generated). We then proceed to study the existence
and uniqueness of a particular class of steady states and examine their relationship to the corresponding class of time-dependent
problems. This enables us to extend the global-existence results, and to indicate consistency between the time-independent and
time-dependent analyses. In order to better understand the effects of distinct temperatures in each phase, a number of our results are
then compared with those of a corresponding single-temperature model.We find that the results coincide in the appropriate limit of
infinite heat-exchange rate. However, when the heat exchange is finite the blowup results can be altered substantially.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/j.nonrwa.2006.12.002
ISSNs: 1468-1218 (print)
Related URLs:
Keywords: porous solid ignition, dual temperature, fluid production, nonlinear parabolic, global existence, blowup, steady states
Subjects: T Technology > TP Chemical technology
Q Science > QA Mathematics
Q Science > QC Physics
Divisions : University Structure - Pre August 2011 > School of Engineering Sciences > Thermofluids and Superconductivity
ePrint ID: 44771
Accepted Date and Publication Date:
April 2008Published
Date Deposited: 15 Mar 2007
Last Modified: 31 Mar 2016 12:18

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