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).

Download

[img] PDF
Download (418Kb)

Description/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: Article
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
Date Deposited: 15 Mar 2007
Last Modified: 27 Mar 2014 18:29
URI: http://eprints.soton.ac.uk/id/eprint/44771

Actions (login required)

View Item View Item

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics