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Abstract In the last few years, the MI-ID stability of fluids problems have received great attention for their crucial applications in various domains of science. Here we study the stability of different geometrical models analytically and numerically taking into account the effect of different external forces such as eJectromagnetic, rotation, seJfgravitational, etc. Chapter (I) is an introduction, a brief discussion of the concept of stability and different techniques which may be used in stability problems analysis are introduced. Also we present the basic hydrodynamics and magnetohydrodynamics equations which are essential for formulating any stability problem. Finally, we review on some reported works which are the foundation of our work In chapter (IT), the stability of a gas jet of zero inertia dispersed in a liquid (hollow jet) has been studied. The desired stability criterion is derived on using Lagrangian non-linear differential equation. The eigenvalue relation is discussed and the results are verified numerically for a11wavenurnbers in various modes of disturbance. Chapter (Ill) is devoted to the MIID instability of an annulus fluid having a very dense liquid (tar) mantle cylinder immersed in a bounded tenuous medium pervaded by a helical varying magnetic field. A general eigenvalue relation is derived and discussed analytically and numerically. Several published stability criteria of different models are obtained as limiting cases from the present general result Many results have been obtained concerning the effects of different parameters such as the streaming and pervading magnetic fields on stabilizing the model. ABSTRACT : HODA AHMED ISMAIL HASHEM. : ”MAGNETOHYDRODYNAMIC STABILITY OF AN ANNULAR FLUID SURROUNDED BY BOUNDED FLUID MEDIUM” : Doctorat of Philosophy in Engineering Mathematics. : Faculty of Engineering, Ain Shams University. : Engineering Physics and Mathematics (Engineering Mathematics). The results are published in the Journal of Applied Mathematics and Computation (USA), 147 (2004), 191-210. In chapter (IV), the self gravitating instability of thermal radiating and rotating gas cloud is investigated. The gas medium is acted by selfgravitating, gas pressure gradient, radiating pressure gradient and rotating forces. The stability criterion has been derived and discussed and the effect of radiation on the gravitational instability of the rotating gas cloud is identified for general wave propagation. The results of this problem are accepted for publication in the Journal of Mathematical Sciences, TB. Center For Science & Technology (India) (2003). Keywords: Magnetobydrodynamics - Stability - Selfgravitating - Hollow Jet - Annular Fluid Jet. |