## Abstract

A solution is developed for a nondiffusive thermal explosion in a reactive gas confined to a bounded container Ω with a characteristic length l'. The process evolves with a spatially homogeneous time-dependent pressure field because the characteristic reaction time t'_{R} is large compared to the acoustic time l'/C'_{0} where C'_{0} is the initial sound speed. Exact solutions, in terms of a numerical quadrature are obtained for the induction period temperature, density and pressure perturbations as well as for the induced velocity field. Traditional single-point thermal runaway singularities are found for temperature and density when the initial temperature disturbance has a single point maximum. In contrast, if the initial maximum is spread over a finite subdomain of Ω, then the thermal runaway occurs everywhere. Asymptotic expansions of the exact solutions are used to provide a complete understanding of the singularities. The perturbation temperature and density singularities have the familiar logarithmic form — ln (t'_{e} — t') as the explosion time l_{e} is approached. The spatially homogeneous pressure is bounded for single-point explosions but is logarithmically singular when global runaway occurs. Compression heating associated with the unbounded perturbation pressure rise is the physical source of the global thermal runaway.

Original language | English (US) |
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Pages (from-to) | 45-62 |

Number of pages | 18 |

Journal | Combustion Science and Technology |

Volume | 63 |

Issue number | 1-3 |

DOIs | |

State | Published - Jan 1 1989 |

## All Science Journal Classification (ASJC) codes

- Chemical Engineering(all)
- Chemistry(all)
- Energy Engineering and Power Technology
- Fuel Technology
- Physics and Astronomy(all)