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July/August 2012 The dynamics of chemical reactors in porous media
Johannes Bruining, Pablo Castañeda, Dan Marchesin
Adv. Differential Equations 17(7/8): 725-746 (July/August 2012).

Abstract

Is ignition or extinction the fate of an exothermic chemical reaction occurring in a bounded region within a heat conductive solid consisting of a porous medium? In the spherical case, the reactor is modeled by a system of reaction-diffusion equations that reduces to a linear heat equation in a shell, coupled at the internal boundary to a nonlinear ODE modeling the reaction region. This ODE can be regarded as a boundary condition. This model allows the complete analysis of the time evolution of the system: there is always a global attractor. We show that, depending on physical parameters, the attractor contains one or three equilibria. The latter case has special physical interest: the two equilibria represent attractors ("extinction" or "ignition") and the third equilibrium is a saddle. The whole system is well approximated by a single ODE, a "reduced" model, justifying the "heat transfer coefficient" approach of Chemical Engineering.

Citation

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Johannes Bruining. Pablo Castañeda. Dan Marchesin. "The dynamics of chemical reactors in porous media." Adv. Differential Equations 17 (7/8) 725 - 746, July/August 2012.

Information

Published: July/August 2012
First available in Project Euclid: 17 December 2012

zbMATH: 1254.80004
MathSciNet: MR2963802

Subjects:
Primary: 35B38, 35B40, 35K55, 35K575, 35K60, 37L25

Rights: Copyright © 2012 Khayyam Publishing, Inc.

JOURNAL ARTICLE
22 PAGES

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Vol.17 • No. 7/8 • July/August 2012
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