Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 935095, 13 pages
doi:10.1155/2008/935095
Research Article
Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates
Department of Mechanical Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran
Received 7 August 2008; Accepted 1 December 2008
Academic Editor: Ben T. Nohara
Copyright © 2008 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
The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM) is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.