### Abstract

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 language | English |
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Pages (from-to) | 509-510 |

Number of pages | 2 |

Journal | ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik |

Volume | 76 |

Issue number | SUPPL. 5 |

Publication status | Published - 1996 |

### ASJC Scopus subject areas

- Computational Mechanics
- Applied Mathematics

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## Cite this

Swift, A., Balakrishnan, E., & Wake, G. C. (1996). Multiple steady state solutions and shape factors for a combustion problem.

*ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik*,*76*(SUPPL. 5), 509-510.