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A comparison of two- and three-variable models for combustion in sealed containers

Published online by Cambridge University Press:  17 February 2009

Claire E. Trenham  and
Larry K. Forbes
Claire E. Trenham
Affiliation:
School of Mathematics and Physics, University of Tasmania, G.P.O. Box 252–37, Hobart 7001 TAS, Australia; e-mail: ctrenham@utas.edu.au.
Larry K. Forbes
Affiliation:
School of Mathematics and Physics, University of Tasmania, G.P.O. Box 252–37, Hobart 7001 TAS, Australia; e-mail: ctrenham@utas.edu.au.
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Abstract

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This paper analyses a model for combustion of a self-heating chemical (such as pool chlorine), stored in drums within a shipping container. The system is described by three coupled nonlinear differential equations for the concentration of the chemical, its temperature and the temperature within the shipping container. Self-sustained oscillations are found to occur, as a result of Hopf bifurcation. Temperature and concentration profiles are presented and compared with the predictions of a simpler two-variable approximation for the system. We study the period of oscillation and its variation with respect to the ambient temperature and the reaction parameter. Nonlinear resonances are found to exist, as the solution jumps between branches having different periods.

Keywords

combustion modelslimit cyclesnonlinear resonancesrelaxation oscillations.
Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 4 , April 2006 , pp. 527 - 540
Copyright
Copyright © Australian Mathematical Society 2006

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