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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 209678, 15 pages
http://dx.doi.org/10.5402/2012/209678
Research Article

Exact Solutions for the Axial Couette Flow of a Fractional Maxwell Fluid in an Annulus

1Abdus Salam School of Mathematical Sciences, GC University, Lahore 54600, Pakistan
2Department of Mathematics, University of Education, Lahore 54000, Pakistan
3Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantt 47040, Pakistan

Received 10 October 2011; Accepted 3 November 2011

Academic Editors: M. Rasetti, A. Sanyal, and G. F. Torres del Castillo

Copyright © 2012 M. Imran 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

The velocity field and the adequate shear stress corresponding to the rotational flow of a fractional Maxwell fluid, between two infinite coaxial circular cylinders, are determined by applying the Laplace and finite Hankel transforms. The solutions that have been obtained are presented in terms of generalized 𝐺 π‘Ž , 𝑏 , 𝑐 ( β‹… , 𝑑 ) and 𝑅 π‘Ž , 𝑏 ( β‹… , 𝑑 ) functions. Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions. The corresponding solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting cases of our general solutions. Finally, the influence of the material parameters on the velocity and shear stress of the fluid is analyzed by graphical illustrations.