Effect of reactant consumption on the induction period and critical condition for a thermal explosion

Abstract

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 spatial varia­tion of temperature is treated by considering only the maximum temperature at the centre of the reacting material and an effective transfer coefficient between the centre and the environment. The results are found to agree satisfactorily with detailed numerical solutions by Rice, Allen & Campbell (1935) and Todes & Melentiev (1939, 1940) where these are applicable. The effect of reactant consumption on the critical value of the explosion para­meter is shown to be more than twice that calculated by Frank-Kamenetskii (1946).