Electromagnetic force calculations for a conical coil
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I.
INTRODUCTION
T O D A Y , the manufacturing industry faces a need to handle very reactive metals and alloys at high temperatures. Due to the reactive nature of these materials, crucible contamination is a serious problem and the purity of the finished product is affected. Therefore, containerless manufacturing and processing techniques to handle these materials have been and are being developed, t~l Many of these containerless processing techniques employ electromagnetic fields. They are based on the fact that an alternating magnetic field can transfer energy to a conducting body without direct contact. Electromagnetic levitation melting is one of the important containerless processing techniques that is used in the manufacturing industry. It was first patented in 1922 by Muck in Germany. Izl Since then, it has been developed to find application in the measurement of hightemperature thermophysical properties, purification of metals, homogenization of alloys, and containerless formation of alloys from elements to avoid crucible contamination. When a conducting body is placed in an alternating magnetic field, eddy currents are induced in it. These eddy currents interact with the external magnetic field to create Lorentz forces on the body. If the Lorentz forces are large enough to oppose gravity, levitation occurs. In addition, the eddy currents cause joule heating in the body and may be used to melt it. Levitation melting has been used to advantage in the development of many containerless thermophysical property measurement techniques for high-temperature liquid metals. Bayazitoglu and co-workers 13-41 suggest a method to measure the thermal diffusivity of hightemperature liquid metals by using levitation melting. Keene et al. jS~ report experiments to measure surface tension of liquid metals. A method of obtaining surface tension and viscosity by observing the damped oscillations of levitated droplets has been developed by Bayazitoglu and Suryanarayana. 16] Margrave t7] recommends a levitation based method to obtain heat capacities of liquid metals over 1500 ~ It is important to note that all o f U D A Y A B. S A T H U V A L L I , Graduate Student, and Y I L D I Z B A Y A Z I T O G L U , Professor of Mechanical Engineering, are with the Mechanical Engineering and Materials Science Department, Rice University, Houston, TX 77005. Manuscript submitted October 14, t992. METALLURGICAL TRANSACTIONS B
the above methods rely on the stable levitation and sub-
sequent melting of a small sample of metal. Most of the literature on levitation melting deals with one or more of the following aspects: calculation of the Lorentz forces on the levitating sample and the power absorbed by it due to joule heating, 18-~zl the analysis of fluid flow in the sample and/or stability considerations (usually via the formulation of a magnetohydrodynamic problem), t~3-2~ and experimental studies and measurement of thermophysical properties. 13 7.21.24.26-301 Frost and Wang 181 developed the theory for a conducting body levitating in a hom
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