Criteria of thermal explosion of chemically reacting systems

A theoretical description of thermal explosion (spontaneous ignition), which occurs in exothermally reacting systems, was provided. The steady-state criterion for thermal explosion to occur was described. By means of perturbation theory, function forms were analysed for the most generalized circumstances in which the Biot number (Bi) is arbitrary and in which the reaction rate is generally represented by f(θ). Asymptotic solutions were derived for the limit of large activation energies where the dimensionless activation energy ε is small (i.e. ε→0). Corresponding critical values for the Frank-Kamenetskii parameters, reduced reaction rate, δ and reduced central temperature-excess, θ₀ given by using these asymptotic equations, were used for obtaining critical temperatures T_m and T_0,cr, where T_m is critical ignition temperature and T_0,cr is the critical (maximum) central temperature, for some typical samples. These results are provided in Tables 5 and 6.