Thermal explosion of autocatalytic reaction

Abstract

Analytical and numerical solutions are used to determine the critical conditions for thermal explosion of autocatalytic reaction. The solutions covers both the reaction governed by the Arrhenius kinetics equation and the Frank-Kamenetskii approximation for that equation. The definition of criticality as the point at which d 2 θ / dβ 2 =0, d 3 θ / dβ 3 =0 and dθ / dβ 〉0 is used here. The study is dealt with low and high exothermicity ( B ) of the reaction and their effects on the critical parameters. The numerical solutions cover the whole reaction from start at β = 0 up to the end at β = 1.0. All trajectories from subcritical, critical to supercritical are offered. The effects of different parameters such as B , ψ and θ a (ambient temperature) on the critical conditions are presented. The results showed that the lower the autocatalytic factor ( β 0 ) is, the pronounced autocatalytic reaction explosion. The analytical solution offered analytical expressions for the critical condition and the different limits of the solutions are clarified. It was found that the numerical results confirm the analytical solution.