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International Journal of Engineering Mathematics
Volume 2014, Article ID 785396, 13 pages
http://dx.doi.org/10.1155/2014/785396
Research Article

Analytical Solutions of Some Fully Developed Flows of Couple Stress Fluid between Concentric Cylinders with Slip Boundary Conditions

1Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440 010, India
2Department of Mathematics, CVR College of Engineering, Hyderabad 501 510, India
3Department of Mathematics, Osmania University, Hyderabad 500 007, India

Received 28 January 2014; Revised 13 May 2014; Accepted 28 May 2014; Published 17 June 2014

Academic Editor: Viktor Popov

Copyright © 2014 M. Devakar 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

We establish, in this paper, the closed form analytical solutions of steady fully developed flows of couple stress fluid between two concentric cylinders, generated due to the constant pressure gradient or the translatory motion of the outer cylinder or both, using the slip boundary conditions. The classical solutions for Newtonian fluid in the hydrodynamic case appear as a limiting case of our solutions. The velocity profiles of the flows are presented and the effect of various parameters on velocity is discussed. The results indicate that the presence of couple stresses decreases the velocity of the fluid.