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Mathematical Problems in Engineering
Volume 2012, Article ID 325423, 12 pages
http://dx.doi.org/10.1155/2012/325423
Research Article

Magnetohydrodynamic Stability of Streaming Jet Pervaded Internally by Varying Transverse Magnetic Field

Basic and Applied Sciences Department, College of Engineering and Technology, Arab Academy for Science & Technology and Maritime Transport (AASTMT), P.O. Box 2033 Elhorria, Cairo, Egypt

Received 9 October 2011; Accepted 12 December 2011

Academic Editor: Alexei Mailybaev

Copyright © 2012 Alfaisal A. Hasan. 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

The Magnetohydrodynamic stability of a streaming cylindrical model penetrated by varying transverse magnetic field has been discussed. The problem is formulated, the basic equations are solved, upon appropriate boundary conditions the eigenvalue relation is derived and discussed analytically, and the results are verified numerically. The capillary force is destabilizing in a small axisymmetric domain 0 < 𝑥 < 1 and stabilizing otherwise. The streaming has a strong destabilizing effect in all kinds of perturbation. The toroidal varying magnetic field interior the fluid has no direct effect at all on the stability of the fluid column. The axial exterior field has strong stabilizing effect on the model. The effect of all acting forces altogether could be identified via the numerical analysis of the stability theory of the present model.