Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 659691, 41 pages
doi:10.1155/2011/659691
Research Article

On the Perturbation of the Three-Dimensional Stokes Flow of Micropolar Fluids by a Constant Uniform Magnetic Field in a Circular Cylinder

Department of Engineering Sciences, University of Patras, 265 04 Patras, Greece

Received 3 June 2010; Accepted 25 January 2011

Academic Editor: Alexander P. Seyranian

Copyright © 2011 Panayiotis Vafeas 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

Modern engineering technology involves the micropolar magnetohydrodynamic flow of magnetic fluids. Here, we consider a colloidal suspension of non-conductive ferromagnetic material, which consists of small spherical particles that behave as rigid magnetic dipoles, in a carrier liquid of approximately zero conductivity and low-Reynolds number properties. The interaction of a 3D constant uniform magnetic field with the three-dimensional steady creeping motion (Stokes flow) of a viscous incompressible micropolar fluid in a circular cylinder is investigated, where the magnetization of the ferrofluid has been taken into account and the magnetic Stokes partial differential equations have been presented. Our goal is to apply the proper boundary conditions, so as to obtain the flow fields in a closed analytical form via the potential representation theory, and to study several characteristics of the flow. In view of this aim, we make use of an improved new complete and unique differential representation of magnetic Stokes flow, valid for non-axisymmetric geometries, which provides the velocity and total pressure fields in terms of easy-to-find potentials. We use these results to simulate the creeping flow of a magnetic fluid inside a circular duct and to obtain the flow fields associated with this kind of flow.