Convective flows on reactive surfaces in porous media

A model for the convective; flow in a fluid-saturated porous medium contain ing a reactive component is considered. This component undergoes an exother mic reaction (modelled by a first order mechanism) on an impermeable boundi ng surface, the resulting heat released driving the convective Bow Large Ra yleigh number Bow near a stagnation point is treated in detail by first con sidering the steady states. Multiple solution branches and critical points arising from a hysteresis bifurcation are identified. The form that these s olution branches take depends on whether or not the effects of reactant con sumption are included. An initial-value problem is then discussed. This sho ws that both the lower (slow reaction) and upper (fast reaction) solution b ranches are stable (and the ultimate state of the system). When the paramet er values are such that there is no steady state, the solution develops a f inite-time singularity, the nature of which is analysed.