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arXiv · 1410.1303

Self-similar analytic solution of the two dimensional Navier-Stokes equation with a non-Newtonian type of viscosity

Imre Ferenc Barna·Gabriella Bognar
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Abstract

We investigate the two dimensional incompressible Navier-Stokes(NS) and the continuity equations in Cartesian coordinates and Eulerian description for non-Newtonian fluids. As a non-Newtonian viscosity we consider the Ladyzenskaya model with a non-linear velocity dependent stress tensor. The key idea is the multi-dimensional generalization of the well-known self-similar Ansatz, which was already used for non-compressible and compressible viscous flow studies. The geometrical interpretations of the trial function is also discussed. We compare our recent results to the former Newtonian ones.

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Imre Ferenc Barna, Gabriella Bognar. 2014-10-06. Self-similar analytic solution of the two dimensional Navier-Stokes equation with a non-Newtonian type of viscosity. https://doi.org/10.3846/13926292.2016.1136901

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