On the unsteady rotational flow of a fractional second grade fluid through a circular cylinder Article

First Online: 26 October 2010 Received: 22 April 2010 Accepted: 12 October 2010 DOI :
10.1007/s11012-010-9373-1

Cite this article as: Athar, M., Kamran, M. & Imran, M. Meccanica (2012) 47: 603. doi:10.1007/s11012-010-9373-1
Abstract Here the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. At time t =0 the fluid is at rest and the motion is produced by the rotation of the cylinder around its axis. The solutions that have been obtained are presented under series form in terms of the generalized G -functions. The similar solutions for ordinary second grade and Newtonian fluids are obtained from general solution for β →1, respectively, β →1 and α _{1} →0. Finally, the influences of the pertinent parameters on the fluid motion, as well as a comparison between models, is underlined by graphical illustrations.

Keywords Generalized second grade fluid Velocity field Shear stress Exact solutions

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Authors and Affiliations 1. Abdus Salam School of Mathematical Sciences GC University Lahore Pakistan