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Journal of Applied Mathematics
Volume 2012, Article ID 804105, 17 pages
http://dx.doi.org/10.1155/2012/804105
Research Article

Effects of Regional Magnetic Field on Rotating MHD Flow Field of Unity Magnetic Prandtl Number

Department of Vehicle Engineering, National Pingtung University of Science and Technology, Pingtung 912, Taiwan

Received 29 January 2012; Revised 30 March 2012; Accepted 16 April 2012

Academic Editor: Hiroshi Kanayama

Copyright © 2012 Sheng Lun Hung and Jik Chang Leong. 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

This work numerically studies the flow pattern of a magnetic fluid filled within an annulus whose inner cylinder is moving at a constant rotational speed, while the outer cylinder is stationary but under the influence of a nonuniform external magnetic field. The magnetic field consists of four basic configurations, that is, completely circular, semicircular, quarter circular, and alternately quarter circular. The strength of the external magnetic field is characterized using a reference Hartmann number. As the reference Hartmann number increases, the fluid elements need to overcome greater resistance to enter the region with magnetic field. Hence, there always exists an apparent recirculation cell within the region without externally applied magnetic field. The strength and size of the recirculation cell depend on the reference Hartmann number, the number and size of the discrete regions without external magnetic field. Only the shear stress on the moving cylinder always increases in magnitude with the reference Hartmann number and the span of the single external magnetic field region. Splitting and separating the external magnetic field may increase the magnitude of the shear stress on the moving inner cylinder but decrease that on the stationary outer cylinder. If the magnitude of the shear stress on the outer cylinder reduces beyond zero, a shear stress in the opposite sense will increase in magnitude with Hartmann number.