Thermal explosion: Escape times in the uniform temperature approximation. Part 2. Perturbations of critical initial conditions

B. F. Gray*, J. H. Merkin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

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 languageEnglish
Pages (from-to)13-26
Number of pages14
JournalMathematical Engineering in Industry
Volume4
Issue number1
Publication statusPublished - 1993
Externally publishedYes

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