Soret-Driven Convection of Non-Newtonian Binary Fluids in a Shallow Cavity Uniformly Heated from Below: Case of Opposing Flows

Abstract

The project under study investigates Soret-generated convection in a horizontal rectangular cavity filled with a non-Newtonian binary fluid. The cavity's two horizontal walls are exposed to uniform fluxes of heat, whereas the two vertical walls are adiabatic and impermeable. The study focuses on the effects of different key parameters, including the cavity aspect ratio (A), the Lewis number (Le), the buoyancy ratio (N), the power-law behavior index (n), the generalized Prandtl (Pr) and thermal Rayleigh (RaT) numbers. The mathematical model, describing the Soret-generated convection phenomenon, is presented by non-linear differential equations, which are solved numerically on the basis of finite volume method. An analytical solution of the problem is proposed derived from the parallel flow approximation in the core of the cavity. The degree of agreement of the numerical finding and analytical predictions is seen to be good. Representative results for the central stream function, Nusselt and Sherwood numbers as well as streamlines, isotherms and iso-concentrations are depicted as functions of the main parameters mentioned above. For opposing flows, the initiation and development of convective motion are explored. The fluid flow's behavior was discovered to be highly influenced by the values of n and N. The beginning of motion is predicted to be governed by supercritical and subcritical Rayleigh numbers.