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

Fetecau, C.; Fetecau, Corina

doi:https://doi.org/10.1155/MPE/2006/23587

Mathematical Problems in Engineering

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Volume 2006 | Article ID 023587 | https://doi.org/10.1155/MPE/2006/23587

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

C. Fetecau¹and Corina Fetecau²

Received02 Feb 2006

Accepted11 Jul 2006

Published28 Jan 2007

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 α1→0, they reduce to those for a Navier-Stokes fluid.

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Copyright

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.

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