Effect of an Oblique Magnetic Field Applied to the Sloshing of Free Surface Waves in the Magnetic Fluid

Abstract

In this paper, linear theory of magnetic fluid sloshing in a rectangular tank subjected to an external oblique magnetic field was studied. Historic of subject as well his importance for fluid mechanics, technology and industrial applications. Magnetic fluid was considered perfect, incompressible and irrotational. Surface tension, gravity and magnetic permeability were taken into account. Linear equations are solved with linear boundary conditions. In the framework of the linear theory, variable separation method makes it possible to construct solutions and obtain eigenfrequencies and the eigen modes. The linear theory is still valid for a very small amplitude of sloshing. The direction and amplitude effects of the external oblique magnetic field on the free surface evolution were analyzed and main results were synthesized. The stability criteria are discussed theoretically and graphically illustrated.