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A NOTE ON WITHDRAWAL FROM A TWO-LAYER FLUID THROUGH A LINE SINK IN A POROUS MEDIUM

Part of: Flows in porous media; filtration; seepage

Published online by Cambridge University Press:  01 July 2008

G. C. HOCKING  and
H. ZHANG
G. C. HOCKING*
Affiliation:
Mathematics and Statistics, Murdoch University, Western Australia 6150, Australia (email: [email protected])
H. ZHANG
Affiliation:
School of Engineering, Gold Coast Campus, Griffith University, Queensland 4222, Australia
*
✉For correspondence.
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Abstract

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The steady response of the free surface of a fluid in a porous medium is considered during extraction of the fluid through a line sink. A conformal-mapping approach is used to derive exact solutions to a family of problems in which the line sink is placed at the apex of a wedge-shaped impermeable base, including the limiting cases of an unbounded aquifer and a flat-bottomed aquifer of finite depth. Both critical cusp solutions and sub-critical solutions are computed exactly as Fourier sine series.

Keywords

porous mediumselective withdrawalhodograph methodexact solutionline sink

MSC classification

Secondary: 76S05: Flows in porous media; filtration; seepage
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 1 , July 2008 , pp. 101 - 110
Copyright
Copyright © Australian Mathematical Society 2009

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