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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 374670, 13 pages
http://dx.doi.org/10.5402/2012/374670
Research Article

Analytical Solutions for the Flow of a Fractional Second Grade Fluid due to a Rotational Constantly Accelerating Shear

1Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantt 47040, Pakistan
2Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
3Department of Mathematics, University of Education, Lahore 54000, Pakistan

Received 7 May 2012; Accepted 25 June 2012

Academic Editors: P. Hogan and G. F. Torres del Castillo

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

Exact analytic solutions are obtained for the flow of a generalized second grade fluid in an annular region between two infinite coaxial cylinders. The fractional calculus approach in the governing equations of a second grade fluid is used. The exact analytic solutions are constructed by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a constantly accelerating shear. The solutions that have been obtained satisfy both the governing equations and all imposed initial and boundary conditions. Moreover, they can be easily specialized to give similar solutions for second grade and Newtonian fluids. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between the three models, is underlined by graphical illustrations.