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

The effects of heat exchange and fluid production on the ignition of a porous solid
The effects of heat exchange and fluid production on the ignition of a porous solid
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.
porous solid ignition, dual temperature, fluid production, nonlinear parabolic, global existence, blowup, steady states
1468-1218
562-584
Shah, A.A.
5c43ac37-c4a7-4256-88ef-8c427886b924
Brindley, J.
8cd03ded-35f6-42b4-88cc-a8fcf86608de
McIntosh, A.
57adedc7-d530-4375-98d2-0c4a551f9b90
Rademacher, J.
822484e9-b237-4d5a-ad90-b56f0c6b7234
Shah, A.A.
5c43ac37-c4a7-4256-88ef-8c427886b924
Brindley, J.
8cd03ded-35f6-42b4-88cc-a8fcf86608de
McIntosh, A.
57adedc7-d530-4375-98d2-0c4a551f9b90
Rademacher, J.
822484e9-b237-4d5a-ad90-b56f0c6b7234

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).

Record type: Article

Abstract

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.

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Published date: April 2008
Keywords: porous solid ignition, dual temperature, fluid production, nonlinear parabolic, global existence, blowup, steady states

Identifiers

Local EPrints ID: 44771
URI: http://eprints.soton.ac.uk/id/eprint/44771
ISSN: 1468-1218
PURE UUID: ef80cca8-00cb-423f-a2b7-23f3a233e627

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Date deposited: 15 Mar 2007
Last modified: 15 Mar 2024 09:07

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Contributors

Author: A.A. Shah
Author: J. Brindley
Author: A. McIntosh
Author: J. Rademacher

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