Steady thermo-diffusive shear Couette flow of incompressible fluid. Velocity field analysis

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Abstract

An exact solution that describes steady flow of viscous incompressible fluid with coupled convective and diffusion effects (coupled dissipative Soret and Dufour effects) has been found. To analyze shear fluid flow an over-determined boundary value problem has been solved. The over-determination of the boundary value problem is caused by the advantage of number of equations in non-linear Oberbeck–Boussinesq system against number of unknown functions (two components of velocity vector, pressure, temperature and concentration of dissolved substance). Non-trivial exact solution of system consisting of Oberbeck–Boussinesq equations, incompressibility equation, heat conductivity equation and concentration equation has been built as Birich–Ostroumov class exact solution. Since the exact solution a priori satisfies the incompressibility equation the over-determined system is solvable. Existence of stagnation points is shown both in general flow and in secondary fluid motion without vorticity. Conditions of countercurrent appearance are found.

About the authors

Vyacheslav Vladimirovich Bashurov

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences; Ural State University of Railway Transport

Email: vbashurov@usurt.ru
ORCID iD: 0000-0003-4711-1894
SPIN-code: 7470-6409
http://www.mathnet.ru/person41772

Cand. Tech. Sci.; Engineer; Sect. of Nonlinear Vortex Hydrodynamics1; Dean of Electrotechnical Faculty2

34, Komsomolskaya st., Ekaterinburg, 620049, Russian Federation; 66, Kolmogorova st., Ekaterinburg, 620034, Russian Federation

Evgeniy Yu. Prosviryakov

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences; Ural State University of Railway Transport

Author for correspondence.
Email: evgen_pros@mail.ru
ORCID iD: 0000-0002-2349-7801
SPIN-code: 3880-5690
Scopus Author ID: 57189461740
ResearcherId: E-6254-2016
http://www.mathnet.ru/person41426

Dr. Phys. & Math. Sci.; Head of Sector; Sect. of Nonlinear Vortex Hydrodynamics1; Professor; Dept. of Natural Sciences2

34, Komsomolskaya st., Ekaterinburg, 620049, Russian Federation; 66, Kolmogorova st., Ekaterinburg, 620034, Russian Federation

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