Table of Contents
ISRN Mathematical Physics
Volume 2012, Article ID 835398, 15 pages
http://dx.doi.org/10.5402/2012/835398
Research Article

Critical Study on Rotational Flow of a Fractional Oldroyd-B Fluid Induced by a Circular Cylinder

1Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantt 47040, Pakistan
2Abdus Salam School of Mathematical Sciences, GC University, Lahore 54600, Pakistan

Received 15 August 2011; Accepted 13 September 2011

Academic Editors: P. Minces and H. Zhou

Copyright © 2012 M. Kamran et al. 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

We considered the unsteady flow of a fractional Oldroyd-B fluid through an infinite circular cylinder with the help of infinite Hankel and Laplace transforms. The motion of the fluid is produced by the cylinder that, at time 𝑡=0+ is subject to a time-dependent angular velocity. The established solutions have been presented under series form in terms of the generalized 𝐺 functions satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, ordinary and fractional Maxwell, ordinary and fractional second-grade, and Newtonian fluids, performing the same motion, are acquired as limiting cases of general solutions. The keynote points regarding this work to mention are that (1) we extracted the expressions for velocity field and shear stress corresponding to the motion of fractional second-grade fluid as a limiting case of general solutions; (2) the expressions for velocity field and shear stress are in the most simplified form in contrast with the studies of Siddique and Sajid (2011), in which the expression for the velocity field involves the convolution product as well as the integral of the product of generalized 𝐺 functions. Finally, numerical results are presented graphically and discussed in order to reveal some physical aspects of obtained results.