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Starting solutions for the motion of second grade fluids due to oscillating shear stresses

Starting solutions for the motion of second grade fluids due to oscillating shear stresses Abstract Exact analytic solutions for the motion of second grade fluid between two infinite coaxial cylinders are established. The motion is produced by the inner cylinder that at time t = 0+ applies torsional and longitudinal oscillating shear stresses to the fluid. The exact analytic solutions, obtained with the help of Laplace and finite Hankel transforms, and presented as a 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 a1 to 0 they reduce to those for a Newtonian fluid. Finally, the effect of various parameters of interest on transient parts of velocity components, velocity profiles as well as comparison between second grade and Newtonian fluids is discussed through graphical illustration. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Engineering de Gruyter

Starting solutions for the motion of second grade fluids due to oscillating shear stresses

Nonlinear Engineering , Volume 4 (2) – Jul 1, 2015

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Publisher
de Gruyter
Copyright
Copyright © 2015 by the
ISSN
2192-8010
eISSN
2192-8029
DOI
10.1515/nleng-2015-0011
Publisher site
See Article on Publisher Site

Abstract

Abstract Exact analytic solutions for the motion of second grade fluid between two infinite coaxial cylinders are established. The motion is produced by the inner cylinder that at time t = 0+ applies torsional and longitudinal oscillating shear stresses to the fluid. The exact analytic solutions, obtained with the help of Laplace and finite Hankel transforms, and presented as a 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 a1 to 0 they reduce to those for a Newtonian fluid. Finally, the effect of various parameters of interest on transient parts of velocity components, velocity profiles as well as comparison between second grade and Newtonian fluids is discussed through graphical illustration.

Journal

Nonlinear Engineeringde Gruyter

Published: Jul 1, 2015

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