The structure of the thermal explosion limit with variable pre-exponential factor

An approximate critical explosion parameter, which separates the slow and explosive reactions is determined with respect to the initial data, using the asymptotic technique to analyze a one step reaction mechanism with temperature dependent pre-exponential factor. We obtained and analysed the effect of the variable pre-exponential factor on the critical temperature, critical parameter for thermal explosion and the first order approximation of the slow curve. By introducing a new coordinate and using the Method of Invariant Manifold (MIM), we obtained corrections on the critical temperature. The results obtained are not only general; they also reveal some salient properties of the system hitherto unknown.