Eur. Phys. J. Plus (2011) 126: 7
https://doi.org/10.1140/epjp/i2011-11007-y

Regular Article

Magnetohydrodynamic stability of an oscillating fluid cylinder

¹ Mathematics Department, Faculty of Science, Ain-Shams University, Cairo, Egypt
² Mathematics Department, Women University College, Ain-Shams University, Cairo, Egypt
³ Basic and Applied Sciences Department, College of Engineering and Technology, Arab Academy for Science & Technology and Maritime Transport (AAST), P.O. Box 2033, Cairo, Egypt

Received: 7 June 2010
Accepted: 21 November 2010
Published online: 19 January 2011

Abstract

The magnetohydrodynamic stability of an oscillating streaming fluid cylinder pervaded by longitudinal magnetic fields has been discussed. The problem is formulated, the basic equations are solved, upon appropriate boundary conditions the non-singular solutions are identified. Moreover, a second-order integro-differential equation in the amplitude of the deflection of perturbation, of Mathieu equation type is derived. The magnetic fields interior and exterior to the fluid have strong stabilizing influences for all perturbation modes. The capillary force is destabilizing only in the small axisymmetric domain while it is stabilizing in all the other domains of perturbation modes. The oscillating streaming of the fluid has a strong stabilizing tendency. The destabilizing character of the model due to the capillary force could be reduced and suppressed, then the stability sets in.