### 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 |
---|---|

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 |

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### ASJC Scopus subject areas

- Computational Mechanics
- Applied Mathematics

### Cite this

*ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik*,

*76*(SUPPL. 5), 509-510.

**Multiple steady state solutions and shape factors for a combustion problem.** / Swift, A.; Balakrishnan, E.; Wake, G. C.

Research output: Contribution to journal › Article

*ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik*, vol. 76, no. SUPPL. 5, pp. 509-510.

}

TY - JOUR

T1 - Multiple steady state solutions and shape factors for a combustion problem

AU - Swift, A.

AU - Balakrishnan, E.

AU - Wake, G. C.

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33747216827&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747216827&partnerID=8YFLogxK

M3 - Article

VL - 76

SP - 509

EP - 510

JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

SN - 0044-2267

IS - SUPPL. 5

ER -