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Mathematical Problems in Engineering
Volume 2006, Article ID 23587, 9 pages
http://dx.doi.org/10.1155/MPE/2006/23587

Starting solutions for some simple oscillating motions of second-grade fluids

1Department of Mathematics, Technical University of Iasi, Iasi 6600, Romania
2Department of Theoretical Mechanics, Technical University of Iasi, Iasi 6600, Romania

Received 2 February 2006; Accepted 11 July 2006

Copyright © 2006 C. Fetecau and Corina Fetecau. 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 exact starting solutions corresponding to the motions of a second-grade fluid, due to the cosine and sine oscillations of an infinite edge and of an infinite duct of rectangular cross-section as well as those induced by an oscillating pressure gradient in such a duct, are determined by means of the double Fourier sine transforms. These solutions, presented as sum of the steady-state and transient solutions, satisfy both the governing equations and all associate initial and boundary conditions. In the special case when α10, they reduce to those for a Navier-Stokes fluid.