Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of Viscosity

Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of Viscosity

We investigate Navier-Stokes (NS) and the continuity equations in Cartesian coordinates and Eulerian description for the two dimensional incompressible nonNewtonian fluids. Due to the non-Newtonian viscosity we consider the Ladyzenskaya model with a non-linear velocity dependent stress tensor. The...

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Bibliographic Details
Main Authors: Imre Ferenc Barna, Gabriella Bognar, Krisztian Hriczo
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2016-01-01
Series:Mathematical Modelling and Analysis
Subjects:
self-similar solution
Ladyzenskaya model
non-Newtonian fluid
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/797
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spelling doaj-169c3298cebb4aaf9f32e26e253ede1f2021-07-02T14:19:42ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102016-01-0121110.3846/13926292.2016.1136901Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of ViscosityImre Ferenc Barna0Gabriella Bognar1Krisztian Hriczo2Wigner Research Center of the Hungarian Academy of Sciences Konkoly-Thege ´ut 29-33, 1121 Budapest, HungaryUniversity of Miskolc 3515 Miskolc-Egyetemv´aros, HungaryUniversity of Miskolc 3515 Miskolc-Egyetemv´aros, Hungary We investigate Navier-Stokes (NS) and the continuity equations in Cartesian coordinates and Eulerian description for the two dimensional incompressible nonNewtonian fluids. Due to the non-Newtonian viscosity we consider the Ladyzenskaya model with a non-linear velocity dependent stress tensor. The key idea is the multidimensional generalization of the well-known self-similar Ansatz, which has already been used for non-compressible and compressible viscous flow studies. Geometrical interpretations of the trial function are also discussed. Our recent results are compared to the former Newtonian ones. https://journals.vgtu.lt/index.php/MMA/article/view/797self-similar solutionLadyzenskaya modelnon-Newtonian fluid
collection DOAJ
language English
format Article
sources DOAJ
author Imre Ferenc Barna
Gabriella Bognar
Krisztian Hriczo
spellingShingle Imre Ferenc Barna
Gabriella Bognar
Krisztian Hriczo
Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of Viscosity
Mathematical Modelling and Analysis
self-similar solution
Ladyzenskaya model
non-Newtonian fluid
author_facet Imre Ferenc Barna
Gabriella Bognar
Krisztian Hriczo
author_sort Imre Ferenc Barna
title Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of Viscosity
title_short Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of Viscosity
title_full Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of Viscosity
title_fullStr Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of Viscosity
title_full_unstemmed Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of Viscosity
title_sort self-similar analytic solution of the two-dimensional navier-stokes equation with a non-newtonian type of viscosity
publisher Vilnius Gediminas Technical University
series Mathematical Modelling and Analysis
issn 1392-6292
1648-3510
publishDate 2016-01-01
description We investigate Navier-Stokes (NS) and the continuity equations in Cartesian coordinates and Eulerian description for the two dimensional incompressible nonNewtonian fluids. Due to the non-Newtonian viscosity we consider the Ladyzenskaya model with a non-linear velocity dependent stress tensor. The key idea is the multidimensional generalization of the well-known self-similar Ansatz, which has already been used for non-compressible and compressible viscous flow studies. Geometrical interpretations of the trial function are also discussed. Our recent results are compared to the former Newtonian ones.
topic self-similar solution
Ladyzenskaya model
non-Newtonian fluid
url https://journals.vgtu.lt/index.php/MMA/article/view/797
work_keys_str_mv AT imreferencbarna selfsimilaranalyticsolutionofthetwodimensionalnavierstokesequationwithanonnewtoniantypeofviscosity
AT gabriellabognar selfsimilaranalyticsolutionofthetwodimensionalnavierstokesequationwithanonnewtoniantypeofviscosity
AT krisztianhriczo selfsimilaranalyticsolutionofthetwodimensionalnavierstokesequationwithanonnewtoniantypeofviscosity
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