Eugeny Prosviryakov
ul. Karla Marksa 10, Kazan, 420111, Russia
Kazan National Research Technical University named after A.N.Tupolev
Publications:
Privalova V., Prosviryakov E. Y.
Steady convective Coutte flow for quadratic heating of the lower boundary fluid layer
2018, Vol. 14, no. 1, pp. 6979
Abstract
This paper presents an exact solution to the Oberbeck – Boussinesq system which describes the flow of a viscous incompressible fluid in a plane channel heated by a linear point source. The exact solutions obtained generalize the isothermal Couette flow and the convective motions of Birikh – Ostroumov. A characteristic feature of the proposed class of exact solutions is that they integrate the horizontal gradient of the hydrodynamic fields. An analysis of the solutions obtained is presented and thus a criterion is obtained which explains the existence of countercurrents moving in a nonisothermal viscous incompressible fluid.

Aristov S. N., Privalova V., Prosviryakov E. Y.
Stationary nonisothermal Couette flow. Quadratic heating of the upper boundary of the fluid layer
2016, Vol. 12, No. 2, pp. 167178
Abstract
A new exact solution of the twodimensional Oberbeck–Boussinesq equations has been found. The analytical expressions of the hydrodynamic fields, which have been obtained, describe convective Couette flow. Fluid flow occurs in the case of nonuniform distribution of velocities and the quadratic heat source at the upper boundary of an infinite layer of viscous incompressible fluid. Two characteristic scales have been introduced for finding the exact solutions of the Oberbeck–Boussinesq equations. Using the anisotropic layer allows one to explore largescale flows of liquids for large values of the Grashof number. A connection is shown between solutions describing the quadratic heating of boundaries with boundary problems concerned with motions of fluids in which the temperature is distributed linearly. Analysis of polynomial solutions describing the natural convection of the fluid is presented. The existence of points at which the hydrodynamic fields vanish inside the fluid layer. Thus, the above class of exact solutions allows us to describe the counterflows in the fluid and the separations of pressure and temperature fields.

Aristov S. N., Prosviryakov E. Y.
Stokes waves in vortical fluid
2014, Vol. 10, No. 3, pp. 309318
Abstract
The solution of the second task of Stokes for the swirled knitting of incompressible liquid is provided. The found solutions represent the elliptic polarized cross waves. The solution of the second Stokes problem for the swirl flow of a viscous incompressible fluid is presented.

Aristov S. N., Prosviryakov E. Y.
Inhomogeneous Couette flow
2014, Vol. 10, No. 2, pp. 177182
Abstract
We have obtained a solution of the problem within the exact solutions of the Navier–Stokes equations which describes the flow of a viscous incompressible fluid caused by spatially inhomogeneous
wind stresses.

Aristov S. N., Prosviryakov E. Y.
On laminar flows of planar free convection
2013, Vol. 9, No. 4, pp. 651657
Abstract
New exact steadystate solutions of the Oberbeck–Boussinesq system which describe laminar flows of the Benard–Marangoni convection are constructed. We consider two types of boundary conditions: those specifying a temperature gradient on one of the boundaries and those specifying it on both boundaries simultaneously. It is shown that when the temperature gradient is specified the problem is essentially twodimensional: there is no linear transformation allowing the flows to be transformed into onedimensional ones. The resulting solutions are physically interpreted and dimensions of the layers are found for which there is no friction on the solid surface and a change occurs in the direction of velocity on the free surface.
