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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 135424, 14 pages
http://dx.doi.org/10.1155/2015/135424
Research Article

Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation

1Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
2School of Computational and Applied Mathematics, DST-NRF Centre of Excellence in Mathematical and Statistical Sciences, Differential Equations, Continuum Mechanics and Applications, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa
3School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

Received 2 August 2014; Accepted 14 September 2014

Academic Editor: Sandile Motsa

Copyright © 2015 M. Khan 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 governing nonlinear equation for unidirectional flow of a Sisko fluid in a cylindrical tube due to translation of the tube wall is modelled in cylindrical polar coordinates. The exact steady-state solution for the nonlinear problem is obtained. The reduction of the nonlinear initial value problem is carried out by using a similarity transformation. The partial differential equation is transformed into an ordinary differential equation, which is integrated numerically taking into account the influence of the exponent n and the material parameter b of the Sisko fluid. The initial approximation for the fluid velocity on the axis of the cylinder is obtained by matching inner and outer expansions for the fluid velocity. A comparison of the velocity, vorticity, and shear stress of Newtonian and Sisko fluids is presented.