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Advances in Mathematical Physics
Volume 2012 (2012), Article ID 634925, 11 pages
http://dx.doi.org/10.1155/2012/634925
Research Article

A Study on the Convergence of Series Solution of Non-Newtonian Third Grade Fluid with Variable Viscosity: By Means of Homotopy Analysis Method

1Department of Mechanical Engineering, University of California Riverside, Bourns Hall, A373, Riverside, CA 92521, USA
2Department of Mathematics & Statistics, FBAS, IIU, H-10, Islamabad 44000, Pakistan

Received 14 December 2011; Accepted 27 January 2012

Academic Editor: Teoman Özer

Copyright © 2012 R. Ellahi. 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

This work is concerned with the series solutions for the flow of third-grade non-Newtonian fluid with variable viscosity. Due to the nonlinear, coupled, and highly complicated nature of partial differential equations, finding an analytical solution is not an easy task. The homotopy analysis method (HAM) is employed for the presentation of series solutions. The HAM is accepted as an elegant tool for effective solutions for complicated nonlinear problems. The solutions of (Hayat et al., 2007) are developed, and their convergence has been discussed explicitly for two different models, namely, constant and variable viscosity. An error analysis is also described. In addition, the obtained results are illustrated graphically to depict the convergence region. The physical features of the pertinent parameters are presented in the form of numerical tables.