Journal of Applied Mathematics
Volume 2012 (2012), Article ID 938624, 13 pages
Research Article

Two-Dimensional and Axisymmetric Unsteady Flows due to Normally Expanding or Contracting Parallel Plates

1Young Researchers Club, Islamic Azad University, Central Tehran Branch, Tehran, Iran
2Mechanical Engineering Department, Islamic Azad University, Central Tehran Branch, Tehran, Iran

Received 17 December 2011; Accepted 22 February 2012

Academic Editor: Md. Sazzad Chowdhury

Copyright © 2012 Saeed Dinarvand and Abed Moradi. 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 for two cases, the two-dimensional flow case and the axisymmetric flow case, is investigated. The governing nonlinear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilizing the homotopy perturbation method (HPM). Graphical results are presented to investigate the influence of the squeeze number on the velocity, skin friction, and pressure gradient. The validity of our solutions is verified by the numerical results obtained by shooting method, coupled with Runge-Kutta scheme.