Energy Based Calculation of the Second-Order Levitation in Magnetic Fluid

Abstract

A permanent magnet immersed in magnetic fluid experiences magnetic levitation force which is of the buoyant type. This phenomenon commonly refers to self-levitation or second-order buoyancy. The stable levitation height of the permanent magnet can be attained by numerical evaluation of the force. Various authors have proposed different computational methods, but all of them rely on force formulation. This paper presents an alternative energy approach in the equilibrium height calculation, which was settled on the minimum energy principle. The problem, involving a cylindrical magnet suspended in a closed cylindrical container full of magnetic fluid, was considered in the study. The results accomplished by the proposed method were compared with those of the well-established surface integral method already verified by experiments. The difference in the results gained by both methods appears to be under 2.5%.

Keywords

• magnetic levitation force
• second-order buoyancy
• magnetic fluid levitation force
• magnetic fluid
• finite element method (FEM)
• surface integral method