Exact Solutions to the Navier–Stokes Equations with Couple Stresses
Autor: | Natalya V. Burmasheva, Evgenii S. Baranovskii, Evgenii Yu. Prosviryakov |
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Rok vydání: | 2021 |
Předmět: |
couple stresses
solvability condition Physics and Astronomy (miscellaneous) overdetermined system General Mathematics exact solutions 01 natural sciences 010305 fluids & plasmas Physics::Fluid Dynamics Overdetermined system Navier–Stokes equations 0103 physical sciences QA1-939 Computer Science (miscellaneous) non-symmetric stress tensor Boundary value problem 0101 mathematics Physics Partial differential equation isobaric flows Cauchy stress tensor Mathematical analysis Hagen–Poiseuille equation micropolar fluid 010101 applied mathematics Shear (sheet metal) Nonlinear system Chemistry (miscellaneous) gradient flows Mathematics |
Zdroj: | Symmetry, Vol 13, Iss 1355, p 1355 (2021) Symmetry Volume 13 Issue 8 |
ISSN: | 2073-8994 |
DOI: | 10.3390/sym13081355 |
Popis: | This article discusses the possibility of using the Lin–Sidorov–Aristov class of exact solutions and its modifications to describe the flows of a fluid with microstructure (with couple stresses). The presence of couple shear stresses is a consequence of taking into account the rotational degrees of freedom for an elementary volume of a micropolar liquid. Thus, the Cauchy stress tensor is not symmetric. The article presents exact solutions for describing unidirectional (layered), shear and three-dimensional flows of a micropolar viscous incompressible fluid. New statements of boundary value problems are formulated to describe generalized classical Couette, Stokes and Poiseuille flows. These flows are created by non-uniform shear stresses and velocities. A study of isobaric shear flows of a micropolar viscous incompressible fluid is presented. Isobaric shear flows are described by an overdetermined system of nonlinear partial differential equations (system of Navier–Stokes equations and incompressibility equation). A condition for the solvability of the overdetermined system of equations is provided. A class of nontrivial solutions of an overdetermined system of partial differential equations for describing isobaric fluid flows is constructed. The exact solutions announced in this article are described by polynomials with respect to two coordinates. The coefficients of the polynomials depend on the third coordinate and time. |
Databáze: | OpenAIRE |
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