ACCOUNTING FOR REACTANT CONSUMPTION IN THE THERMAL-EXPLOSION PROBLEM - 3 - CRITICALITY CONDITIONS FOR THE ARRHENIUS PROBLEM

The rigorously defined criticality condition established by the author s is applied to the Arrhenius model. The dependence of the critical te mperature theta on both the ambient temperature theta(a) and the orde r of reaction n is demonstrated. All solutions for theta as a functio n of theta(a) for any value of n pass through the point of theta(a) = 0.25, theta = 0.5 (the transition point for n = 0). It is shown that a transition temperature exists for all degrees of reaction except for 0 < n less than or equal to 1.0. For a first order reaction, theta m onotonically increases with the ambient temperature and reaches infini ty at theta(a) = 0.5. For 0 < n less than or equal to 1.0, no solution exists for theta > 1/2(1 - n), no transition temperature exists, and the solution for theta as a function of theta(a) passes through an i nflection point at theta(a) = 0.25, theta = 0.5. It is also shown tha t there is significant difference between the results obtained from th e Arrhenius model and those from the Frank-Kamenetskii approximated mo del. The critical state in the theta-tau plane is found to be subcriti cal in both the theta-Z and the psi-theta planes. which produce ident ical results. Proof is provided that criticality in the theta-tau plan e coincides with that in the theta-Z and psi-theta planes only when n = 0 or B = infinity. The criticality limits with different ambient te mperature theta(a) for zero order reaction (n = 0) are established. Th e solution also treats various initial conditions for a zero order rea ction. (C) 1998 by The Combustion Institute.