Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 867906, 11 pages
doi:10.1155/2008/867906
Research Article
Steady Flow of a Second-Grade Fluid in an Annulus with Porous Walls
Mechanical Engineering Department, Faculty of Mechanical Engineering, Istanbul Technical University, Gümüşsuyu 34437, Istanbul, Turkey
Received 22 June 2007; Accepted 9 February 2008
Academic Editor: Kumbakonam Rajagopal
Copyright © 2008 M. Emin Erdoğan and C. Erdem İmrak. 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
An exact solution of an incompressible second-grade fluid for flow between two coaxial cylinders with porous walls is given. It is assumed that the inner cylinder is rotating with a constant angular velocity and the outer one is at rest. The solution is expressed in terms of the confluent hypergeometric functions and it is valid for all values of the cross-Reynolds number and the elastic number. The solutions for −2, +∞, and −∞ values of the cross-Reynolds number are obtained and a comparison with those of the Newtonian fluid is given. Furthermore, the torque exerted by the fluid on the inner cylinder is calculated. It is shown that the moment coefficient depends on the cross-Reynolds number, the elastic number, and the ratio of the radii of the cylinders. The variation of the moment coefficient with these numbers is discussed.