Abstract:
A model of thermal explosion and methods of elementary catastrophe theory were used to study the characteristics of a catastrophe manifold (ignition manifold) and to reveal the qualitative behavior of the solution of Cauchy's problem with variation of the bifurcational parameter. A correspondence between Semenov's critical conditions in the theory of thermal explosion and a catastrophe manifold was established. The conditions of transcendental equation solvability were investigated to determine the kinetic constants ($E$ and $K$). The nonuniqueness of activation energy determination for a given preexponent was shown. A unique solution in which both of the parameters are unknown was deduced. A satisfactory decription of the ignition manifold was obtained for large and small particle radii in the framework of the general ignition criterion. It was demonstrated that as the Nusselt number and ambient temperature increase, the ignition delays calculated using the models of surrounding film and thermal explosion approach one another.
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