Volume 2, Issue 2, November 2016, Page: 13-27

Effect of Wall Conductivity on an Electric Conducting Fluid Flow Between Rotating and Stationary Coaxial Disks in the Presence of a Uniform Axial Magnetic Field

Toshio Tagawa, Department of Aerospace Engineering, Tokyo Metropolitan University, Tokyo, Japan

Received: Sep. 20, 2016;
Accepted: Oct. 14, 2016;
Published: Nov. 8, 2016

DOI: 10.11648/j.fm.20160202.11 View 3343 Downloads 76

Abstract

Numerical analyses have been carried out for magnetohydrodynamic flow between a rotating and a stationary disk, whose radii are sufficiently large in comparison with the gap between the two parallel coaxial disks. The gap is filled with an electric conducting fluid and a uniform axial magnetic field is imposed. The magnetic Prandtl number is assumed to be so small that the influence of the induced magnetic field is neglected. The flow depends on both the rotational Reynolds number and the Hartmann number as well as the wall conductance ratios of upper and lower disks. As the Reynolds number increases, the core region of rigid body rotation having slight axial component of velocity is observed between the two boundary layers, whose thickness becomes thinner in proportional to the square root of the Reynolds number. On the other hand, as the Hartmann number increases, the Lorentz force tends to suppress the secondary flow significantly and boundary layer thickness of the azimuthal component of velocity is proportional to the inverse of the Hartmann number. The derived boundary condition for the normal component of electric current density at the interface allows us to obtain similarity solutions for various combinations of each wall conductance ratio and its influence on the flow is quite significant.

Keywords

Magnetohydrodynamics, Similarity Solution, Secondary Flow, Hartmann Number, Rotating Disk, Wall Conductance Ratio

To cite this article

Toshio Tagawa,
Effect of Wall Conductivity on an Electric Conducting Fluid Flow Between Rotating and Stationary Coaxial Disks in the Presence of a Uniform Axial Magnetic Field,

*Fluid Mechanics*. Vol. 2, No. 2, 2016, pp. 13-27. doi: 10.11648/j.fm.20160202.11Copyright

Copyright © 2016 Authors retain the copyright of this article.

This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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