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The effects of heat exchange and fluid production on the ignition of a porous solid
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Shah, Akeel A., Brindley, J., McIntosh, A. C. and Rademacher, J. (2008) The effects of heat exchange and fluid production on the ignition of a porous solid. Nonlinear Analysis: Real World Applications, Vol.9 (No.2). pp. 562-584. doi:10.1016/j.nonrwa.2006.12.002 ISSN 1468-1218.
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Official URL: http://dx.doi.org/10.1016/j.nonrwa.2006.12.002
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.
Item Type: | Journal Article | ||||
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Subjects: | T Technology > TA Engineering (General). Civil engineering (General) T Technology > TJ Mechanical engineering and machinery |
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Divisions: | Faculty of Science, Engineering and Medicine > Engineering > Engineering | ||||
Journal or Publication Title: | Nonlinear Analysis: Real World Applications | ||||
Publisher: | Elsevier Ltd. | ||||
ISSN: | 1468-1218 | ||||
Official Date: | April 2008 | ||||
Dates: |
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Volume: | Vol.9 | ||||
Number: | No.2 | ||||
Number of Pages: | 23 | ||||
Page Range: | pp. 562-584 | ||||
DOI: | 10.1016/j.nonrwa.2006.12.002 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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