On the steady states of distributed parameter systems with chemical reactions, heat, and mass transfer

The number of steady states for a distributed system with chemical reactions, heat, and mass transfer is investigated by means of fixed point methods. The main step in the analysis is the establishment of a priori bounds for the steady state concentrations and temperature. Such bounds can be derived from the conservation of atomic species and energy, independently of the reaction rates and the size of the medium. It is shown in great generality that steady states exist and they are odd in number. Improved bounds obtained by considering the reaction rates and the size of the medium are used in developing criteria for the uniqueness of the steady state. It is shown that if the medium is sufficiently small there is one only steady state. An example of two second order simultaneous exothermic chemical reactions in a catalyst particle is treated in detail and numerical results are obtained