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On the explosion of chain-thermal reactions

Published online by Cambridge University Press:  17 February 2009

R. O. Ayeni
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Abstract

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A chain reaction of oxygen (reactant) and hydrogen (active intermediary) with mtrosyl chloride (sensitizer) as a catalyst may be modelled mathematically as a non-isothermal reaction. In this paper we present an asymptotic analysis of a spatially homogeneous model of a non-isothermal branched-chain reaction. Of particular interest is the so-called explosion time and we provide an upper bound for it as a function of the activation energy which can vary over all positive values. We also establish a bound on the temperature when the activation energy is finite.

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 2 , October 1982 , pp. 194 - 202
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Ayeni, R. O., “Criteria for branched-chain explosion”, Nigerian J. of Natural Sciences (to appear).Google Scholar
[2]Boddington, T., Gray, P. and Wake, G. C., “Criteria for thermal explosions with and without reactant consumption”, Proc. Roy. Soc. London Set. A 357 (1977), 403–422.Google Scholar
[3]Dainton, F. S., Chain reactions: an introduction (Wiley, New York, 1966).Google Scholar
[4]Gray, P. and Harper, M. J., “Thermal explosions: part 1—induction periods and temperature changes before spontaneous ignition”, Trans. Faraday Soc. 55 (1959), 581–590.CrossRefGoogle Scholar
[5]Kapila, A. K., “Homogeneous branched-chain explosion: initiation to completion”, J. Engrg. Math. 12 (1978), 221–235.Google Scholar
[6]Kondratiev, V. N., The theory of kinetics (Elsevier, New York, 1969), pages 81–188.Google Scholar
[7]Ludford, G. S. S., “Combustion: basic equations and peculiar asymptotics”, J. Mécanique 16 (1977), 531–551.Google Scholar
[8]Mulcahy, M. F. R., Gas kinetics (Nelson, London, 1973).Google Scholar
[9]Pao, C. V., ‘Non existence of global solutions and bifurcation analysis for a boundary value problem of parabolic type”, Proc. Amer. Math. Soc. 65 (1977), 245–251.Google Scholar
[10]Satinger, D. H., “A nonlinear parabolic system in the theory of combustion”, Quart. Appl. Math. 33 (1975), 47–61.Google Scholar