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The Quarterly Journal of Mechanics and Applied Mathematics 1978 31(1):99-112; doi:10.1093/qjmam/31.1.99
© 1978 by Oxford University Press
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THE INFLUENCE OF REACTANT CONSUMPTION ON THE CRITICAL CONDITIONS FOR HOMOGENEOUS THERMAL EXPLOSIONS

D. R. KASSOY and A. LIŅAN

( Mechanical Engineering Department, University of Colorado Boulder, Colorado
Escuela T. S. de Ingenieros Aeronauticas, Universidad Politecnica de Madrid Madrid, Spain )

The spatially homogeneous model of a high activation energy thermal explosion is studied when the heat loss parameter a is close to the classically-defined critical value a = e. Asymptotic solutions are developed which describe the time-history of the temperature and reactant depletion. It is shown that there is a critical time period, large with respect to the characteristic conduction time, in which the temperature variation is described by a Riccati equation. The solution properties of this nonlinear equation permit one to define a value of {Delta} = a – e which separates subsequent subcritical and supercritical behaviour.


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