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

Abstract
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.