Stationary-state solutions for coupled reaction–diffusion and temperature-conduction equations II. Spherical geometry with Dirichlet boundary conditions

Abstract

The stationary-state heat and mass transfer equations for an exothermic process following first-order kinetics and an Arrhenius temperature dependence in a spherical reaction zone may show an infinite number of solutions. Precise numerical computations for a particular case realizes this high multiplicity and determines the evolution of the shape of the temperature–position and reaction–rate–position profiles as a bifurcation parameter λ is varied. With Dirichlet boundary conditions, there is an initial concentration of self heating and reaction close to the centre of the reaction zone. This concentration is enhanced as the central temperature excess increases. At high temperature excesses and with large λ , however, the profiles flatten out, giving rise to sharp boundary layers close to the edge of the sphere.