In the present paper a theoretical description of thermal explosion (spontaneous ignition)

which occurs in exothermically reacting systems

in provided. The steady-state criterion for thermal explosion to occur is described. By means of perturbation theory

functional forms are 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 are 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

θ_0 given by using these asymptotic equations

are used for obtaining critical temperatures T_m and T_0

cr

where T_m is critical ignition temperature and T_0

cris the critical (maximum ) central temperature

for some typical samples. These results are provided in Tables 5 and 6.