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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 285809, 19 pages
http://dx.doi.org/10.1155/2011/285809
Research Article

Spectral Approximation of an Oldroyd Liquid Draining down a Porous Vertical Surface

1Department of Mathematics, University of Gaziantep, 27310 Gaziantep, Turkey
2Department of Elementary Mathematics Education, Mevlana University, 42003 Konya, Turkey
3Department of Mathematics, Nigde University, 51240 Nigde, Turkey

Received 29 June 2011; Revised 5 October 2011; Accepted 10 October 2011

Academic Editor: Carlo Piccardi

Copyright © 2011 F. Talay Akyildiz 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

Consideration is given to the free drainage of an Oldroyd four-constant liquid from a vertical porous surface. The governing systems of quasilinear partial differential equations are solved by the Fourier-Galerkin spectral method. It is shown that Fourier-Galerkin approximations are convergent with spectral accuracy. An efficient and accurate algorithm based on the Fourier-Galerkin approximations for the governing system of quasilinear partial differential equations is developed and implemented. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. The effect of the material parameters, elasticity, and porous medium constant on the centerline velocity and drainage rate is discussed.