Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of Viscosity. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Barna, Imre Ferenc; Bognár, Gabriella; Hriczó, Krisztián
• Is Part Of: Mathematical modelling and analysis. Volume 21:Issue 1(2016)
• Page Start: 83
• Page End: 94
• Publication Date: 2016-01-02
• Subjects: self-similar solution -- Ladyzenskaya model -- non-Newtonian fluid; 34B09 -- 35Q30; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2016.1136901
• Languages: English
• ISSNs: 1392-6292

Abstract

Abstract: We investigate Navier-Stokes (NS) and the continuity equations in Cartesian coordinates and Eulerian description for the two dimensional incompressible non-Newtonian 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.