Some theoretical problems related to flows induced in liquid metals by linear motors

Abstract

We obtain results which describe the electromagnetic (EM) field and some aspects of the fluid flow induced in a liquid metal by a linear induction motor. The need for a theoretical description of the motor and its influence arises from recent developments in the production of flat glass. The EM equations are simplified by initially assuming the liquid metal (which we refer to as 'the conductor') moves as a solid. In this way we include some magnetohydrodynamic effects in the partially coupled hydrodynamic and EM differential equations.
In chapter one we describe the float glass process, provide a physical description of a linear motor, discuss the appropriate EM and hydrodynamic equations and give a survey of the relevant literature. In chapter two we describe an experiment in which liquid mercury is induced to move under the action of a linear motor. In chapter three we derive expressions for a simplified model of a linear motor and obtain velocity profiles for a given Hartmann number. This work is extended in chapter four to include the effect of a superimposed shear flow. In chapters five and six we describe the EM boundary layer region of the conductor. Two- dimensional numerical results are obtained in chapters seven and nine for the EM field induced in the conductor. In chapter eight we examine the flow induced by a rectangular body force, of constant magnitude at a fixed depth, decaying exponentially into the conductor. Chapter eleven extends the magnetic dipole analysis of chapter ten and gives three-dimensional numerical results for'the EM field induced in the conductor by a linear motor. Some aspects of the results of chapters two (the experiment) ten and eleven are discussed in chapter twelve using magnetic field line theory.