Abstract
The paper studies a Couette–Poiseuille exact solution for describing inhomogeneous steady-state flows of a viscous incompressible vertical vortex fluid. The fluid moves in an infinite horizontal layer, this motion being conditioned by the displacement of the lower boundary and the specification of the pressure gradient. An exact solution to the hydrodynamics equations describing the three-dimensional inhomogeneous Couette–Poiseuille shear flow is obtained. It is polynomial in all the coordinates, and it belongs to the Lin–Sidorov–Aristov family. Consideration of the inhomogeneity of the velocity field leads to the recording of counterflows. Pressure variation along the horizontal coordinates results in an additional stationary stagnation point as compared to the isobaric flow of a viscous incompressible fluid.
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