### Abstract

The propagation of a premixed laminar flame supported by an exothermic chemical reaction under adiabatic conditions but subject to inhibition through a parallel endothermic chemical process is considered. The temporal stability to longitudinal perturbations of any resulting flames is investigated. The heat loss through the endothermic reaction, represented by the dimensionless parameter α, has a strong quenching effect on wave propagation. The wave speed-cooling parameter (α, c) curves are determined for a range of values of the other parameters. These curves can be monotone decreasing or S-shaped, depending on the values of the parameters β, representing the rate at which inhibitor is consumed relative to the consumption of fuel, μ, the ratio of the activation energies of the reactants and the Lewis numbers. This gives the possibility of having either one, two or three different flame velocities for the same value of the cooling parameter α. For Lewis numbers close to unity, when there are three solutions, two of them are stable and one is unstable, with two saddle-node bifurcation points on the (α, c) curve. For larger values of the Lewis numbers there is a Hopf bifurcation point on the curve, dividing it into a stable and an unstable branch. The saddle-node and Hopf bifurcation curves are also determined. The two curves have a common, Takens-Bogdanov bifurcation point.

Original language | English |
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Pages (from-to) | 175-203 |

Number of pages | 29 |

Journal | IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications) |

Volume | 69 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 2004 |

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### Keywords

- Evans function
- Multiple solutions
- Quenching
- Travelling wave

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)*,

*69*(2), 175-203. https://doi.org/10.1093/imamat/69.2.175