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

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<sup>-1</sup>), 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<sup>-1</sup>). This is in strong contrast to the times to ignition calculated previously for such perturbations from the critical condition which are of O(δ<sup>-1/2</sup>) . The practical consequences of this difference for the `hot stacking problem' are discussed with respect to the practical occurrence of spontaneous combustion.