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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  and
KAREN M. HASTIE
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
*
✉miccal.matthews@ecu.edu.au
✉khastie0@gmail.com
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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.

Keywords

channel flowslipNavier boundary conditionfinite elementpenalty method
Type
Research Article
Information
The ANZIAM Journal , Volume 53 , Issue 4 , April 2012 , pp. 321 - 336
Copyright
Copyright ©2013 Australian Mathematical Society

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