Critical Conditions of a Thermal Explosion in the Case of Autocatalytic Combustion with Account Reagent and Oxidant Consumption

The work deals with the classical problem of the critical conditions for self–ignition of a gas mixture. The authors presents a reasonably general combustion model that takes into account the consumption of the reactant and oxidizer. The model allows for fractional degrees of reaction orders, including the possibility of taking into account autocatalysis by the reactant and oxidizer. We consider parameters characterizing the heat transfer and the ambient temperature as a control actions. The work pays special attention to the first-order autocatalytic reaction for the reactant. The study shows that control actions can change combustion modes from slow burnout to thermal explosion. Using the technique of invariant manifolds and canards, asymptotic formulas for the critical value of the control parameter are obtained. We point out the exceptionally high sensitivity of the model to changes in the control parameter near its critical value.