Unidirectional Marangoni–Poiseuille flows of a viscous incompressible fluid with the Navier boundary condition

The paper announces a family of exact solutions to Navier–Stokes equations describing gradient inhomogeneous unidirectional fluid motions (nonuniform Poiseuille flows). The structure of the fluid motion equations is such that the incompressibility equation enables us to establish the velocity defect law for nonuniform Poiseuille flow. In this case, the velocity field is dependent on two coordinates and time, and it is an arbitrary-degree polynomial relative to the horizontal (longitudinal) coordinate. The polynomial coefficients depend on the vertical (transverse) coordinate and time. The exact solution under consideration was built using the method of indefinite coefficients and the use of such algebraic operations was for addition and multiplication. As a result, to determine the polynomial coefficients, we derived a system of simplest homogeneous and inhomogeneous parabolic partial equations. The order of integration of the resulting system of equations was recurrent. For a special case of steady flows of a viscous fluid, these equations are ordinary differential equations. The article presents an algorithm for their integration. In this case, all components of the velocity field, vorticity vector, and shear stress field are polynomial functions. In addition, it has been noted that even without taking into account the thermohaline convection (creeping current) all these fields have a rather complex structure.

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Unidirectional Marangoni–Poiseuille flows of a viscous incompressible fluid with the Navier boundary condition

Cited by 3 publications

References 12 publications

A layered unidirectional flow of a viscous incompressible fluid induced in a closed layer by a nonuniform distribution of temperature and pressure fields, with allowance for the perfect slip condition

A layered unidirectional flow of a viscous incompressible fluid induced in a closed layer by a nonuniform distribution of temperature and pressure fields, with allowance for the perfect slip condition

A New Class of Exact Solutions of the Oberbeck–Boussinesq Equations Describing an Incompressible Fluid

Exact Solutions to Navier–Stokes Equations Describing a Gradient Nonuniform Unidirectional Vertical Vortex Fluid Flow

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