Table of Contents
ISRN Mathematical Physics
Volume 2012 (2012), Article ID 831063, 17 pages
http://dx.doi.org/10.5402/2012/831063
Research Article

First Problem of Stokes for Generalized Burgers' Fluids

1Abdus Salam School of Mathematical Sciences, GC University, Lahore 54600, Pakistan
2Department of Mathematics, NED University of Engineering and Technology, Karachi 75270, Pakistan

Received 11 October 2011; Accepted 31 October 2011

Academic Editors: I. Radinschi and W.-H. Steeb

Copyright © 2012 Muhammad Jamil. 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 velocity field and the adequate shear stress corresponding to the first problem of Stokes for generalized Burgers’ fluids are determined in simple forms by means of integral transforms. The solutions that have been obtained, presented as a sum of steady and transient solutions, satisfy all imposed initial and boundary conditions. They can be easily reduced to the similar solutions for Burgers, Oldroyd-B, Maxwell, and second-grade and Newtonian fluids. Furthermore, as a check of our calculi, for small values of the corresponding material parameters, their diagrams are almost identical to those corresponding to the known solutions for Newtonian and Oldroyd-B fluids. Finally, the influence of the rheological parameters on the fluid motions, as well as a comparison between models, is graphically illustrated. The non-Newtonian effects disappear in time, and the required time to reach steady-state is the lowest for Newtonian fluids.