An analytical solution for the stationary behaviour of binary mixtures and pure fluids in a horizontal annular cavity

This study aims at analysing the characteristics of the two-dimensional flow established by binary mixtures and pure fluids in a horizontal annular cavity isothermally heated inside and cooled outside. Some complications arise considering binary mixtures, as a consequence of thermogravitational diffusion due to the coupling of convection with thermodiffusion. An analytical model has been defined assuming a two-dimensional laminar flow of a visco-elastic fluid, under validity of Boussinesq’s assumption and negligible viscous dissipation. For the case of binary mixtures, the buoyancy determined by concentration variations has been ignored, so that momentum equation is independent on concentration and is only coupled with the energy balance equation. The analytical model has been validated, for both cases of binary mixtures and pure fluids, through comparison with numerical results in a wide range of the non-dimensional parameters that govern the problem. In particular, the effect of the geometry and of the boundary conditions on the separation of the mixture compounds due to thermogravitational diffusion has been exploited.