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A Note on the Transient Solution of Stokes' Second Problem with Arbitrary Initial Phase

Published online by Cambridge University Press:  05 May 2011

C.-M. Liu  and
I.-C. Liu
C.-M. Liu*
Affiliation:
General Education Center, Chienkuo Technology University, Changhua Hsien, Taiwan 50094, R.O.C
I.-C. Liu*
Affiliation:
Department of Civil Engineering and Institute of Earthquake and Disaster Mitigation, National Chi Nan University, Nantou Hsien, Taiwan 54561, R.O.C.
*
*Assistant Professor
**Professor
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Abstract

The flow of a viscous fluid disturbed by an oscillating plate of arbitrary initial phase is studied in present note. The exact solutions of the velocity and the shear stress are solved using a Laplace transform method. The velocity is derived in terms of complementary error functions and the shear stress on the boundary is given in the form of Fresnel integrals. Since the steady-state solutions are well known, our discussions are focused on the transient solutions. The transient state will disappear faster for the wall stress than that for the velocity field. Comparing the results corresponding to different initial phases, the cosine case reaches to the steady state more rapidly than the sine case.

Keywords

Stokes' second problemTransient solutionWall shear stress
Type
Technical Note
Information
Journal of Mechanics , Volume 22 , Issue 4 , December 2006 , pp. 349 - 354
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2006

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