CRITICAL CONDITIONS FOR A SPATIALLY-DEPENDENT EXOTHERMIC CHEMICAL REACTION

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Abstract
A first-order exothermic reaction which has a large activation energy takes place within a medium which allows diffusion of the rate-controlling reactant. It is assumed that there is no flux of the reactant through the surface bounding the medium. The initial concentration of the reactant is taken to be uniform. The temperature and concentration are found as asymptotic expansions for ε → 0 where 1/ε is the dimensionless activation energy. The critical initial concentration Ycr, above which a rapid rise in temperature occurs and below which the temperature can only increase moderately is found in the form

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