Instability and bifurcation analysis for an exothermic surface reaction with diffusive heat and mass transfer

The steady distributions of temperature and concentration in a reactive fluid adjacent to a catalytic wall are investigated. It is shown that for the mass action kinetics considered, the number of steady solutions is either one or three. Several simple sufficient criteria, as well as a slightly more complicated necessary and sufficient criterion, are given for the uniqueness of the steady solution. If the Lewis number Le (ratio of molecular and thermal diffusivities) is at least one, then a steady state that is unique is always stable with respect to small disturbances. For Le ≥ 1, the high and low temperature steady states are stable when the number of steady states is three. When Le < 1, even a unique steady state can be unstable, and when there are three steady states, one, two, or three of them can be unstable. The Le ≥ 1 and Le < 1 cases are further distinguished by the fact that oscillatory instability can occur for Le < 1 but not for Le ≥ 1.