## Abstract

For the Semenov model of a single exothermic reaction, which leads to simple thermal explosion theory, the `time to ignition' from a perturbed critical initial condition is calculated. In general, this turns out to be of O(lnδ^{-1}), where δ is a (dimensionless) perturbation to a (dimensionless) unstable steady-state temperature. However, close to criticality this time to ignition is shown to be much longer, of O(δ^{-1}). This is in strong contrast to the times to ignition calculated previously for such perturbations from the critical condition which are of O(δ^{-1/2}) . The practical consequences of this difference for the `hot stacking problem' are discussed with respect to the practical occurrence of spontaneous combustion.

Original language | English |
---|---|

Pages (from-to) | 13-26 |

Number of pages | 14 |

Journal | Mathematical Engineering in Industry |

Volume | 4 |

Issue number | 1 |

Publication status | Published - 1993 |

Externally published | Yes |