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The influence of reactant consumption on the critical conditions for homogeneous thermal explisions
Kassoy, D.R. and Liñán Martínez, Amable
The influence of reactant consumption on the critical conditions for homogeneous thermal explisions.
"Quarterly Journal of Mechanics and Applied Mathematics", v. 31
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 A = a — e which separates subsequent subcritical and supercritical behaviour.
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