REACTIVE-DIFFUSE SYSTEMS WITH ARRHENIUS KINETICS - MULTIPLE SOLUTIONS, IGNITION AND EXTINCTION

The steady reactive-diffusive problem for a nonisothermal porous pellet with first-order exothermic Arrhenius kinetics is studied. In the large activation energy limit, asymptotic solutions are derived for the cylindrical and slab geometries. Analytical expressions for the solution are given on all three branches of the S-curve which characterizes the response of the system. In particular, explicit formulae are obtained for the multiplicity bounds (ignition and extinction limits). Our leading-order asymptotic results are then compared with the results of numerical computations.