Reactive-diffusive equation with variable pre-exponential factor

摘要

We consider the steady-state solutions for the exothermic chemical reaction, taking the diffusion of the reactant in a slab into account and assuming an Arrhenius temperature dependence with variable pre-exponential factor. We solve the resulting nonlinear boundary value problem using both numerical and analytical methods. This new analytical solution for the Frank-Kamenetskii parameter delta, as it is in terms of Bernoulli's numbers, is in accordance with the numerical integration provided the activation energy parameter epsilon (much less than 1) is very small and for epsilon --> 0 it goes to the well-known Frank-Kamenetskii case. We determine numerically the transitional values of delta, epsilon and the dimensionless central temperature theta(m). (C) 2003 Elsevier Ltd. All rights reserved.