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Journal of Applied Mathematics
Volume 2014, Article ID 191606, 14 pages
http://dx.doi.org/10.1155/2014/191606
Research Article

Boundary Layer Flow due to the Vibration of a Sphere

Department of Mathematics, Dammam Community College, KFUPM, P.O. Box 5084, Dhahran 31261, Saudi Arabia

Received 28 April 2014; Accepted 10 July 2014; Published 24 July 2014

Academic Editor: Michael Meylan

Copyright © 2014 Muhammad Adil Sadiq. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Boundary layer flow of the Newtonian fluid that is caused by the vibration of inner sphere while the outer sphere is at rest is calculated. Vishik-Lyusternik (Nayfeh refers to this method as the method of composite expansions) method is employed to construct an asymptotic expansion of the solution of the Navier-Stokes equations in the limit of high-frequency vibrations for Reynolds number of . The effect of the Stokes drift of fluid particles is also considered.