Abstract
ABSTRACTThe 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.
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