The effects of heat exchange and fluid production on the ignition of a porous solid
type: Item
instance of: scholarly article
title: The effects of heat exchange and fluid production on the ignition of a porous solid
zbMATH Open document ID: 1144.80007
author: A. A. Shah
author: A. C. McIntosh
author: J. Brindley
author: Jens D. M. Rademacher
published in: Nonlinear Analysis. Real World Applications
publication date: 2008-05-16T00:00:00Z
full work available at URL: heatexchangeNA.pdf
review text: The authors consider a combustion model when a solid fuel decomposes in an exothermic reaction in fluid and solid products. The authors here allow different temperatures in the fluid and in the solid parts. They write the balance equations which describe the evolution of the temperature, that of the volume fraction of the solid fuel and that of the density of the fluid part. Darcy's law is assumed in the fluid part. The problem is posed in a (\( n+1\)) dimensional parabolic cylinder. Dirichlet boundary conditions are imposed on the lateral boundary of the parabolic cylinder. Initial conditions are imposed at \(t=0\). The authors first introduce adimensional parameters. Then they assume, among other hypotheses, that the system is close to the ambient initial stage, which means that the unknowns or initial data take small perturbations around their initial values. The final problem is a coupled system of nonlinear parabolic equations involving five parameters. The authors prove a local in time existence and uniqueness result for this problem with a possible blow up behaviour in finite time. The authors then describe steady-state solutions in some particular case. The paper ends with a comparison between the solution of this model and that of comparable other models.
reviewed by: Alain Brillard
Mathematics Subject Classification ID: 80A25
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 76V05
zbMATH DE Number: 5276136
zbMATH Keywords: porous solid ignition
zbMATH Keywords: dual temperature
zbMATH Keywords: fluid production
zbMATH Keywords: nonlinear parabolic equation
zbMATH Keywords: global existence
zbMATH Keywords: blowup
zbMATH Keywords: steady states
Wikidata QID: Q56806483
MaRDI profile type: Publication
OpenAlex ID: W2058689377
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DOI: 10.1016/J.NONRWA.2006.12.002
description: scientific article; zbMATH DE number 5276136