REACTIVE-DIFFUSIVE SYSTEM WITH ARRHENIUS KINETICS - PECULIARITIES OF THE SPHERICAL GEOMETRY

The steady reactive-diffusive problem for a nonisothermal permeable pellet with first-order Arrhenius kinetics is studied. In the large activation-energy limit, asymptotic solutions are derived for the spherical geometry. The solutions exhibit multiplicity, and it is shown that a suitable choice of parameters can lead to an arbitrarily large number of solutions, thereby confirming a conjecture based upon past computational experiments. Explicit analytical expressions are given for the multiplicity bounds (ignition and extinction limits). The asymptotic results compare very well with those obtained numerically, even for moderate values of the activation energy.