Journal of Mathematical Chemistry

, Volume 47, Issue 2, pp 790–807 | Cite as

Approximate critical conditions in thermal explosion theory for a two-step kinetic model

Original Paper


Approximate critical conditions for a thermal explosion problem is developed for a two-step reactions based on theories of Semenov and Frank-Kamenetskii. The aim is to examine the contributions of the radical termination step and the temperature dependent pre-exponential factor on the critical parameters within the framework of classical stationary and non-stationary theories. In the non-stationary case, a more general expression for the critical Semenov parameter (Ψ cr ) and critical temperature (θ cr ) were obtained by asymptotic procedure. In the stationary case, numerical estimates for the critical Frank-Kamenetskii parameter (δ cr ) and the critical temperature (θ cr ) were obtained by variational method technique. It was observed that the Semenov and Frank-Kamenetskii parameters are greatly influenced by the termination step and the variable pre-exponential factor. Apart from elucidating hitherto unknown features in the theory of thermal explosion, the results are more general as some known results are easily recovered.


Thermal explosion Asymptotic procedure Two-step reaction Radical termination 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsBen-Gurion University of NegevBeer-ShevaIsrael
  2. 2.Department of MathematicsObafemi Awolowo UniversityIle IfeNigeria

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