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A method of ignition conditions determination for any type of exothermic reaction is proposed. The method is based on the maximum temperatures equation for any kind of kinetic function, which was obtained using the integral equation for phase trajectories. In this case, the asymptotic ignition criterion is defined by the infinitely high sensitivity of maximum temperature to the change of parameters at the limit of ignition. Hence, the critical ignition conditions are determined by the presence of extreme points on the plane: parameter – maximal temperature. On the strength of these ideas, the universal algebraic set of equations for critical conditions calculation for arbitrary kinetic law of reaction product formation was obtained. The application of this method to calculation of the second order reactions allows to define the thermal explosion degeneration conditions and the regions of critical conditions existence. The maximum discrepancy between the results obtained with the results of numerical calculation does not exceed ten percent.

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In this paper, the comparative analysis of the thermal explosion (TE) critical conditions on the planes temperature-conversion degree and temperature-time was conducted. It was established that the ignition criteria are almost identical only at relatively small values of Todes parameter. Otherwise, the results of critical conditions analysis on the plane temperature-conversion degree may be wrong. The asymptotic method of critical conditions calculation for the first-order reactions was proposed (taking into account the reactant consumption). The degeneration conditions of TE were determined. The calculation of critical conditions for specific first-order reaction was made. The comparison of the analytical results obtained with the results of numerical calculations and experimental data showed that they are in good agreement.