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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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References

1.Schlichting, H., Boundary Layer Theory, 7th ed., McGraw-Hill, New York (1979).Google Scholar
2.Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press, New York (1967).Google Scholar
3.Panton, R., “The Transient for Stokes's Oscillating Plate: a Solution in Terms of Tabulated Functions,” J. Fluid Mech., 31(4), pp. 819–825 (1968).Google Scholar
4.Erdogan, M. E., “A Note on an Unsteady Flow of a Viscous Fluid due to an Oscillating Plane Wall,” Int. J. Nonlinear Mech., 35, pp. 1–6 (2000).CrossRefGoogle Scholar
5.Liu, I. C. and Kong, C. H., “Heat Transfer of an Electrically Conducting Viscoelastic Fluid over a Strectching Sheet,” Journal of Mechanics, 21, pp. 5–13 (2005).Google Scholar
6.Liu, I. C., “Exact Solutions for a Fluid-Saturated Porous Medium with Heat and Mass Transfer,” Journal of Mechanics, 21, pp. 57–62 (2005).CrossRefGoogle Scholar
7.Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, Dover, New York (1964).Google Scholar