Approximate critical conditions in thermal explosion theory for a two-step kinetic model
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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.
KeywordsThermal explosion Asymptotic procedure Two-step reaction Radical termination
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- 3.S.O. Ajadi, V. Gol’dshtein , The structure of the thermal explosion limit with variable pre-exponential factor. Russian J. Phys. Chem. B (Accepted) (2009)Google Scholar
- 11.Griffiths J.F., Barnard J.A.: Flame and Combustion. Blackie Academic and Professional, 3rd edn. imprint of Chapman and Hall, London (1995)Google Scholar
- 16.Mishchenko E.F., Rozov N.K.: Differential Equations with Small Parameters and Relaxation. Plenum Press, New York and London (1980)Google Scholar
- 18.Peters N.: Fifteen Lecture on Laminar and Turbulent Combustion. Ercoftac Summer School, Aachen, Germany (1992)Google Scholar
- 20.Todes G.M., Melentiese P.V.: Theory of thermal explosion. J. Phys. Chem. 13(7), 52–58 (1939)Google Scholar
- 21.Wu H., Morbidelli M., Varma A.: An Approximate criterion for reactor thermal runaway. Chem. Eng. Sci. 53(18), 3341–3344 (1988)Google Scholar
- 22.Ya Zeldovich B., Barenblatt G.I., Librovich V.B., Makhviladze G.M.: The Mathematical Theory of Combustion and Explosion. Consultants Bureau, New York (1985)Google Scholar
- 23.M.I. Zharkov, E.F. Mishchenko, N.K. Rozov, On some special functions and constants appeared in theory of relaxation oscillations. Proc. Acad. USSR 261, No. 6 (in Russian) (1981)Google Scholar