### Abstract

The asymptotic solution of the nonlinear ordinary differential equation with two-point boundary conditions which describes a steady diffusion flame in a chamber is considered. The solution is characterized by the unburnt fuel fraction R as a function of the fuel injection rate M. The shape of the corresponding response curve depends on the Damkoehler number D (representing either the constant chamber pressure or the chamber's length) for which two critical values, D//o and D//a, are uncovered. For D greater than D//a the only possibility is R identically 1 (extinguished states). When D//a less than D less than D//o, a closed curve called an isola is also a possible response, its base lying on R equals O (complete burning). As D approaches D//a the isola shrinks to a point and disappears. But when D is increased towards D//o it expands until its left side swells into the end of the strip M greater than O, O less than R less than 1. Then it breaks and joins the extinguished response (which is now limited on the left) to form an S, which is the nature of the response when D greater than D//o. The transitions between the various responses require special asymptotics which are also described herein.

Original language | English (US) |
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Pages (from-to) | 107-123 |

Number of pages | 17 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 37 |

Issue number | 1 |

DOIs | |

State | Published - 1979 |

Externally published | Yes |

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

*SIAM Journal on Applied Mathematics*,

*37*(1), 107-123. https://doi.org/10.1137/0137007