Volume no :65, Issue no: 1, March (2021)

Journal of Mathematical Sciences: Advances and Applications

CORRELATION BETWEEN NO-SLIP AND SLIP BOUNDARY CONDITIONS ASSOCIATED WITH A TWO-DIMENSIONAL NAVIER-STOKES FLOWS IN A PLANE DIFFUSER

Author's: Ranis Ibragimov and Vesselin Vatchev
Pages: [1] - [23]
Received Date: March 04, 2021
Submitted by:
DOI: http://dx.doi.org/10.18642/jmsaa_7100122194

Abstract

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.

Keywords

Navier-Stokes flows, plane diffuser, effects of viscosity, slip boundary conditions.