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AN ANALYTICAL AND NUMERICAL STUDY OF UNSTEADY CHANNEL FLOW WITH SLIP

Published online by Cambridge University Press:  08 February 2013

MICCAL T. MATTHEWS*
Affiliation:
School of Engineering, Edith Cowan University, Joondalup, WA 6027, Australia
KAREN M. HASTIE*
Affiliation:
School of Engineering, Edith Cowan University, Joondalup, WA 6027, Australia
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Abstract

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A theoretical investigation of the unsteady flow of a Newtonian fluid through a channel is presented using an alternative boundary condition to the standard no-slip condition, namely the Navier boundary condition, independently proposed over a hundred years ago by both Navier and Maxwell. This boundary condition contains an extra parameter called the slip length, and the most general case of a constant but different slip length on each channel wall is studied. An analytical solution for the velocity distribution through the channel is obtained via a Fourier series, and is used as a benchmark for numerical simulations performed utilizing a finite element analysis modified with a penalty method to implement the slip boundary condition. Comparison between the analytical and numerical solution shows excellent agreement for all combinations of slip lengths considered.

Type
Research Article
Copyright
Copyright ©2013 Australian Mathematical Society

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