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Exact analytical solution based on the vector potential technique for a conjugated hydrodynamic and joule heating problem in an electromagnetically levitated drop

S. Lomaev1 - M. Krivilyov2 - J. Fransaer1

1 KU Leuven, Department of Materials Engineering, Kasteelpark Arenberg 44, 3001~Heverlee, Belgium
2 Department of Physics, Udmurt State University, 1 Universitetskaya str., 426034 Izhevsk, Russia

The paper presents exact analytical expressions for Lorentz force density and Joule heat power induced by an external alternating electric current inside a magnetically levitated drop. These expressions have been written as the source right-hand-side terms in the analytic solution for the stream function and temperature which were derived previously using Van Dyke's series-truncation technique. For the first time, a close-form analytical solution for the conjugated hydrodynamic and thermal problems for a spherical drop surrounded by gas was obtained. This method is a robust and fast approach for the evaluation of fluid flow and temperature fields in levitation experiments on rapid solidification of metals. Figs 2, Refs 17.

Magnetohydrodynamics 52, No. 1/2, 105-116, 2016 [PDF, 0.51 Mb]

Copyright: Institute of Physics, University of Latvia
Electronic edition ISSN 1574-0579
Printed edition ISSN 0024-998X