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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 531250, 18 pages
http://dx.doi.org/10.5402/2012/531250
Research Article

Stability of Compressible Hollow Jet Pervaded by a Transverse Varying Magnetic Field

1Department of Mathematics, Women's University College, Ain Shams University, Asmaa Fahmy Street, Heliopolis, Cairo 11566, Egypt
2Department of Engineering Physics and Mathematics, Faculty of Engineering, Ain Shams University, Cairo 11566, Egypt
3Department of Basic and Applied Sciences, College of Engineering and Technology, Arab Academy for Science & Technology and Maritime Transport (AAST), P.O. Box 2033, Elhorria, Cairo 11361, Egypt
4Department of Engineering Physics and Mathematics, Faculty of Engineering (Mataria), Helwan University, Cairo 11321, Egypt

Received 13 October 2011; Accepted 16 November 2011

Academic Editor: G. Cleaver

Copyright © 2012 Samia S. Elazab 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

The magnetohydrodynamic stability of an ordinary compressible hollow cylinder pervaded by a transverse varying magnetic field, under the influence of capillary, inertia, and Lorentz force, has been developed. The problem is modelized. The basic equations formulated, solved, and, upon applying appropriate boundary conditions, the singular solutions are excluded. The eigenvalue relation has been derived and discussed. The capillary force has destabilizing influence only for long wavelengths in the axisymmetric perturbation but it is stabilizing in the rest and also so in the nonaxisymmetric perturbations. The compressibility increases the stable domains and simultaneously decreases those of instability. The electromagnetic force has different effects due to the axial uniform field and varying transverse one. The axial field is stabilizing for all wavelengths in all kinds of perturbations. The transverse field is stabilizing or not according to restrictions. Here, the high compressibility increases rapidly the magnetodynamic stable domains and leads to shrinking those of instability.