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Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn


Correlation between No-slip and Slip Boundary Conditions Associated with a Two-dimensional Navier-Stokes Flows in a Plane Diffuser

Journal of Vibration Testing and System Dynamics 6(2) (2022) 235--246 | DOI:10.5890/JVTSD.2022.06.005

Ranis Ibragimov, Vesselin Vatchev

Department of Mathematics, Wenatchee Valley College, 1300 Fifth St, Wenatchee, WA 98801

School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, One West Boulevard, Brownsville, TX 78520

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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.

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