REACTIVE-DIFFUSE SYSTEMS WITH ARRHENIUS KINETICS: MULTIPLE SOLUTIONS, IGNITION AND EXTINCTION.

A. K. Kapila; B. J. Matkowsky

doi:10.1137/0136028

REACTIVE-DIFFUSE SYSTEMS WITH ARRHENIUS KINETICS: MULTIPLE SOLUTIONS, IGNITION AND EXTINCTION.

A. K. Kapila^*, B. J. Matkowsky

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

The steady reactive-diffusive problem for a nonisothermal porous pellet with first-order exothermic Arrhenius kinetics is studied. In the large activation energy limit, asymptotic solutions are derived for the cylindrical and slab geometries. Analytical expressions for the solution are given on all three branches of the S-curve which characterizes the response of the system. In particular, explicit formulae are obtained for the multiplicity bounds (ignition and extinction limits). Our leading-order asymptotic results are then compared with the results of numerical computations.

Original language	English (US)
Pages (from-to)	373-389
Number of pages	17
Journal	SIAM J Appl Math
Volume	36
Issue number	2
DOIs	https://doi.org/10.1137/0136028
State	Published - Jan 1 1979

ASJC Scopus subject areas

Applied Mathematics

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abstract = "The steady reactive-diffusive problem for a nonisothermal porous pellet with first-order exothermic Arrhenius kinetics is studied. In the large activation energy limit, asymptotic solutions are derived for the cylindrical and slab geometries. Analytical expressions for the solution are given on all three branches of the S-curve which characterizes the response of the system. In particular, explicit formulae are obtained for the multiplicity bounds (ignition and extinction limits). Our leading-order asymptotic results are then compared with the results of numerical computations.",

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AB - The steady reactive-diffusive problem for a nonisothermal porous pellet with first-order exothermic Arrhenius kinetics is studied. In the large activation energy limit, asymptotic solutions are derived for the cylindrical and slab geometries. Analytical expressions for the solution are given on all three branches of the S-curve which characterizes the response of the system. In particular, explicit formulae are obtained for the multiplicity bounds (ignition and extinction limits). Our leading-order asymptotic results are then compared with the results of numerical computations.

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REACTIVE-DIFFUSE SYSTEMS WITH ARRHENIUS KINETICS: MULTIPLE SOLUTIONS, IGNITION AND EXTINCTION.

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