ANZIAM  J.  47 (2006), 527-540

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

Claire E. Trenham   School of Mathematics and Physics   University of Tasmania   G.P.O. Box 252--37   Hobart 7001 TAS   Australia     ctrenham@utas.edu.au and Larry K. Forbes   School of Mathematics and Physics   University of Tasmania   G.P.O. Box 252--37   Hobart 7001 TAS   Australia

Abstract

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.

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