Open AccessCorrelation between No-Slip and Slip Boundary Conditions Associated with A Two-Dimensional Navier-Stokes Flows in a Plane Diffuser
Author(s) -
Ranis N. Ibragimov,
AUTHOR_ID,
Vesselin Vatchev,
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Publication year - 2021
Publication title -
journal of mathematical sciences : advances and applications
Language(s) - English
Resource type - Journals
ISSN - 0974-5750
DOI - 10.18642/jmsaa_7100122194
Subject(s) - slip (aerodynamics) , boundary value problem , perturbation (astronomy) , mechanics , mathematical analysis , no slip condition , mathematics , navier–stokes equations , physics , geometry , mixed boundary condition , compressibility , thermodynamics , quantum mechanics
We examine the viscous effects of slip boundary conditions for the model describing two-dimensional Navier-Stokes flows in a plane diffuser. It is shown that the velocity profile is related to a half period shifted Weierstrass function with two parameters. This allows to approximate the explicit solution by a Taylor series expansion with two new micro- parameters, that can be measured in physical experiments. It is shown that the assumption for no-slip boundary conditions is stable in the sense that a small perturbation of the boundary values result in a small perturbation in the solutions.