The sublimation of an electrically conducting droplet through the use of an external alternating magnetic field
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I.
INTRODUCTION
T H E electromagnetic sublimation of a conducting body requires the solution of the Maxwell equations for electrodynamics along with the Navier-Stokes equations for fluid flow coupled through Ohm's law for moving media. In addition, equations of phase change and free surface geometry must be formulated. Due to extremely rapid heating rates, interface velocities may be high enough to consider nonequilibrium sublimation. Also, if the surrounding medium is deemed to be participating, solution of the radiative transfer equation is required. Our model will use several simplifying assumptions in order to make this a more tractable problem. The problem of fluid flow in a conducting liquid of given surface shape under the influence of an alternating magnetic field has been studied by Moffatt~] and Sneyd.t2.3] Mestel analyzed liquid metal levitating in an alternating magnetic field to determine the free surface geometry and velocity field.t4] A voluminous amount of work has also been done in the area of absorbed power and Lorentz forces on conducting bodies exposed to an alternating magnetic field. Rony determined the power absorption and the levitation force for a conducting sphere exposed to a homogeneous alternating magnetic field.[s] Fromm and Jehn, in a more detailed model using a series of stacked current carrying loops to model the field, calculated the power absorption and levitation forces for a conducting sphere.t6] Lohofer derived power absorption for a levitating body exposed to an arbitrary but sinusoidally varying magnetic field.t7] Vaporization and sublimation phase change considerations as a result of Joule heating, however, have received little attention. In 1964, Van Audenhove gave a description and resuits for an experimental technique of vacuum evaporation of metals by high frequency levitation heating3sJ Vutsens provided both an analytical expression and experimental data for a levitating drop of aluminum in a solenoid of unspecified geometry.tg] More recent studies by Bayazitoglu and Cemy consider an electrically conducting drop of liquid metal of finite conductivity undergoing nonequilibrium vaporization.El~ Bayazitoglu and Cerny have also consid-
VICTOR G. STICKEL, Jr., Graduate Student, and YILDIZ BAYAZITOGLU, Professor of Mechanical Engineering, are with the Mechanical Engineering and Materials Science Department, Rice University, Houston, TX 77005. Manuscript submitted June 16, 1994. METALLURGICAL AND MATERIALS TRANSACTIONS B
ered an infinite conductivity model undergoing nonequilibrium vaporization.till In this article, we examine both analytically and experimentally the heating and subsequent sublimation of a small electrically conducting body caused by the Joule heating effect associated with an alternating magnetic field. The body is stationary, sublimating in vacuum and undergoing radiative heat loss. Equations are developed for energy conservation and phase change and careful attention is paid to the modeling of the alternating magnetic field so as to incorporate importan
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