Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 935095, 13 pages
Research Article

Analytic Approximate Solutions for Unsteady Two-Dimensional and Axisymmetric Squeezing Flows between Parallel Plates

Mohammad Mehdi Rashidi, Hamed Shahmohamadi, and Saeed Dinarvand

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.


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.