Fire Safety Science Digital Archive

An approximate theoretical analysis is given of a thermal explosion or ignition. The treatment leads to analytic expressions for the effect of reactant consumption on the critical explosion parameter and the induction period for a theoretical model where spacial variation of temperature is neglected, i.e. where it is treated in terms of an effective transfer coefficient. The results are found to agree satisfactorily in a certain range with the more detailed. analyses leading to graphical solutions by Rice, Allen and Campbell and Todes and Melentiev. The effect of reactant consumption on the critical value of the explosion parameter is shown to be about twice that calculated by Frank-Kamenetskii. In particular it is shown that for a heat of reaction of 100 cal/gm and an activation energy of about 25,000 cal/mole - values typical for the self heating and ignition of fibre insulating boards - there is a significant effect of reactant consumption on the induction period if the explosion or ignition parameter is less than about twice the critical value calculated assuming no reactant loss.