Allowance for mutual effect of ‘Hot spots’ in solution of problems of site thermal explosion

Local effect of intensification of substance heating depending on the distance between 'hot spots' is studied within the framework of a site thermal explosion in the case of a zeroth-order reaction. A combination of the values of the Arrhenius number Ar, Frank-Kamenetskii criterion Fk, distance between 'hot spots' a, and their width w at which two nearest points give a nonlinear effect of local intensification of the total heating of a substance is found. The method is based on the use of an approximate analytical solution of the corresponding Cauchy problem which is presented in the form of asymptotic expansion in terms of Poincare.[PUBLICATION ABSTRACT]