The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion

Abstract

This paper concerns the laminar flows which arise in fluids due to the interaction of the force of gravity and density differences caused by the simultaneous diffusion of thermal energy and of chemical species. Species concentration levels are assumed small, as is typical for many processes in water and in atmospheric air. The usual Boussinesq approximations yield a set of equations which are shown to have solutions of similarity form for combined buoyancy effects, for vertical flows adjacent to surfaces and in plumes. This similarity is of the same form as that found for single buoyancy mechanism flows. The resulting equations were integrated for air and water for various practical values of the Schmidt number and for multiple buoyancy effects aiding and opposing. The results show many interesting effects on velocity, heat and mass transfer, and on laminar stability. A comparison of the results with those of integral method analysis shows the limits and reasons for failure of these approximate calculations in the more complicated of such combined buoyancy mechanism flows.