Exact Solutions for Steady Convective Layered Flows with a Spatial Acceleration

In this paper, we study non-one-dimensional convective layered flows of a viscous incompressible fluid with a spatial acceleration. We perform the simulation on the base of thermal convection equations in the Boussinesq approximation. We seek for solutions to these equations in a generalized class of exact solutions, where all components of the velocity vector, the pressure, and the temperature represent complete linear forms of two Cartesian coordinates with nonlinear (with respect to to the third Cartesian coordinate) coefficients. We prove that the system of correlations that describe layered flows can be reduced to an overdetermined system of ordinary differential equations. We state and prove two theorems that justify the existence (under a special algebraic condition) and uniqueness of the solution to the resulting overdetermined system.