Two-component convection flow driven by a heat-releasing concentration field

Abstract

In this work we study the convection flow driven by a heat-releasing concentration field which itself is stably stratified. The heat-releasing rate is linearly proportional to concentration. Linear stability analysis is conducted to determine the critical heat-releasing rate for given fluid properties and concentration differences. The most unstable mode associated with the critical heat-releasing rate can be oscillatory for a large concentration Rayleigh number, i.e. the non-dimensionalized concentration difference and large Schmidt number, i.e. the ratio of viscosity to diffusivity of the concentration component. Fully developed flows are then investigated by direct numerical simulations. Flow structures near the bottom plate have larger horizontal scales than those near the top plate. The concentration in the bulk is almost constant and takes a similar value for all the explored parameters, which results in the convective flux increasing linearly with height. To explain the dependences of the global transport properties, we extend the unifying theory of the Rayleigh–Bénard convection to the current system and develop scaling laws for the global fluxes. The numerical results can be described accurately by the theoretical model.