Multiple steady state solutions and shape factors for a combustion problem

A. Swift*, E. Balakrishnan, G. C. Wake

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We investigate multiple steady state solutions of the heat balance equation for material undergoing an exothermic reaction over some closed region, using dimensionless form of the relevant steady state reaction-diffusion equation. Arrhenius kinetics are assumed and two cases considered, namely, the well known Frank-Kamenetskii approximation ("old" variable case) and the "new" variable approach of Burnell et al. In each case, we show that there exist multiple solutions. Further more, a well known approximate method gives a different number of solutions than a direct solution method in each of these two cases.

Original languageEnglish
Pages (from-to)509-510
Number of pages2
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Issue numberSUPPL. 5
Publication statusPublished - 1996
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics


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