Linear analysis of the dispersion relation of surface waves of a magnetic fluid in a square container under an external oblique magnetic field

In this study, free surface evolution of a magnetic fluid in a finite size tank which is subjected to an external magnetic field was investigated. The physical problem and equations governing fluid motion and magnetic field were given with boundary conditions. Using proper selection of variables, dimensionless equation system governing magnetic fluid sloshing were written. Resolution method based on multiple scale variables was presented and solution of the linear problem was given. The dispersion relation obtained in the finite depth case was compared with that corresponding to an infinite depth calculated with the same assumptions. Direction and magnitude of the external magnetic field, magnetic permeability ratio and surface tension effects on magnetic fluid free surface stability were analysed and important results were discussed.