Studying the concentration field distribution in shear concentration convective flows of a viscous incompressible fluid in a plane horizontal layer with immobile boundaries

Abstract

Depending on the reasons causing changes in the density of a fluid, it is customary to distinguish between thermal convection and concentration-induced convection. The phenomenon of concentration-induced convection often accompanies the flow of a working fluid in devices working, for example, with fluid coolants. When modeling such flows, the consideration of the generalization of the Boussinesq hypothesis assuming the dependence of the fluid density on the impurity concentration and on the temperature of the fluid itself leads to the situation that the flow velocity field and the concentration field affect each other. The paper investigates the features of the shear convective flow of a viscous incompressible fluid with an admixture in the horizontal layer. The system of concentration-induced convection equations consisting of the equation of motion of a viscous fluid, the concentration change equation, and the incompressibility condition is taken as a system of defining relations. The solution is sought in the class of functions linear in two coordinates (x and y). As the boundary conditions, it is assumed that the no-slip condition is met at the lower impermeable boundary, that the upper boundary of the layer is immobile, and that the distribution of salinity and pressure is specified on it. A complete solution of the boundary value problem is given. The attention is focused on the analysis of the distribution of the concentration field inside the fluid layer. It is shown that, according to the solution of the boundary value problem for the concentration field, its homogeneous (with respect to the horizontal coordinates) component does not vanish inside the layer. The components of the concentration field, linearly dependent on the horizontal coordinates, take a constant value everywhere inside the layer. The change in the mutual arrangement of the isolines of the concentration field at the transition from one section of the fluid layer to another is studied. Relevant findings are illustrated.