Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 706840, 18 pages
doi:10.1155/2010/706840
Research Article

Application of Homotopy Analysis Method to the Unsteady Squeezing Flow of a Second-Grade Fluid between Circular Plates

Mohammad Mehdi Rashidi,1 Abdul Majid Siddiqui,2 and Mostafa Asadi1

1Department of Mechanical Engineering, Faculty of Engineering, Bu Ali Sina University, P.O. Box 65175-4161, Hamedan, Iran
2Department of Mathematics, Pennsylvania State University, York Campus, York, PA 17403, USA

Received 17 September 2010; Accepted 23 November 2010

Academic Editor: Victoria Vampa

Copyright © 2010 Mohammad Mehdi Rashidi 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 investigated an axisymmetric unsteady two-dimensional flow of nonconducting, incompressible second grade fluid between two circular plates. The similarity transformation is applied to reduce governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE) in dimensionless form. The resulting nonlinear boundary value problem is solved using homotopy analysis method and numerical method. The effects of appropriate dimensionless parameters on the velocity profiles are studied. The total resistance to the upper plate has been calculated.