Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-15T11:19:02.962Z Has data issue: false hasContentIssue false
  • English
  • Français

The Unsteady Viscous Flow Generated by an Oscillating Porous Plate

Published online by Cambridge University Press:  05 May 2011

C.-M. Liu ,
H.-H. Hwung  and
C.-H. Kong
C.-M. Liu*
Affiliation:
General Education Center, Chienkuo Technology University, Changhua, Taiwan 50094, R.O.C.
H.-H. Hwung*
Affiliation:
Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
C.-H. Kong*
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Associate Professor, correspondence author
**Professor
**Professor
Get access

Abstract

The flow of a viscous still fluid disturbed by an oscillating porous plate with an arbitrary initial phase is investigated. Using the Laplace transform, the exact solution of the velocity profile is revisited. Subsequently, the wall stress implying the required driving force is derived in this study. The solutions are valid not only for large times but also for small times. Four special cases are discussed to investigate the influences of four parameters on the development of the flow. A dimensionless analysis for general cases is also provided. Our analyses significantly stress on the following subjects. Firstly, the porous velocity and the decay factor affecting the development of the flow are studied. Secondly, the occurrence time of separation and the corresponding critical condition are investigated. The period of the transient velocity influenced by the Reynolds number and the initial phase is discussed. Present study includes many existing solutions as special cases. Results can be also applied to many engineering problems with the same PDE form and boundary conditions. In conclusion, this study presents the detailed discussions and the magnitude of the required driving force which were missed in previous works.

Keywords

Transient periodSeparationPorous velocityDecay factorAngular frequencyInitial phase.
Type
Articles
Information
Journal of Mechanics , Volume 24 , Issue 2 , June 2008 , pp. 145 - 152
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Batchelor, G. K.,An Introduction to Fluid Dynamics, Cambridge University Press, New York (1967).Google Scholar
2.Schlichting, H., Boundary Layer Theory, McGraw- Hill Book Company, New York (1979).Google Scholar
3.Panton, R., “The Transient for Stokes’ Oscillating Plate: A Solution in Terms of Tabulated Functions,” J. Fluid Mech., 31, pp. 819–825 (1968).CrossRefGoogle Scholar
4.Erdogan, M. E., “A Note on an Unsteady Flow of a Viscous Fluid Due to an Oscillating Plane Wall,” Int. J. Non-Linear Mech., 35, pp. 1–6 (2000).CrossRefGoogle Scholar
5.Liu, C. M. and Liu, I. C., “A Note on the Transient Solution of Stokes’ Second Problem with Arbitrary Initial Phase,” Journal of Mechanics, 22, pp. 349–354 (2006).CrossRefGoogle Scholar
6.Turbatu, S., Bühler, K. and Zierep, J., “New Solutions of the II. Stokes Problem for an Oscillating Flat Plate,” ActaMech., 129, pp. 25–30 (1998).Google Scholar
7.Ashraf, E. E. and Mohyuddin, M. R., “New Solutions of Stokes Problem for an Oscillating Plate Using Laplace Transform,” J. Appl. Sci. Environ. Mgt., 9, pp. 51–55(2005).Google Scholar
8.Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, Dover Publication, Inc., New York (1964).Google Scholar