A Couette-type flow with a perfect slip condition on a solid surface

On the basis of a system of hydrodynamic equations, the unidirectional steady flow of a viscous incompressible fluid in a horizontal extended layer is studied. The solution to the governing equations is discovered in a distinguished class of functions that are linear in coordinates.
The contact of the fluid with a lower hydrophobic solid boundary is described by the Navierslip condition. At the upper boundary of the layer, the temperature and pressure fields are assumed to be given, and a zero shear stress is specified. The system of boundary conditions is redefined due to the fact that all conditions for velocities are assigned as their derivatives. Zero flow rate is taken as an additional condition.
The obtained exact solution to the boundary value problem is the only possible polynomial solution. The highest (eighth) degree of polynomials corresponds to a solution for background pressure. Analysis of the solution shows that it can describe a multiple stratification of kinetic-force fields.
Since the analysis is carried out in a general form (without specifying physical constants that uniquely identify the fluid under study), the obtained results are applicable to viscous fluids of different nature.