A perturbational approach to magneto-thermal problems of a deformed sphere levitated in a magnetic field

ISSN： 0022-0833

Source： Journal of Engineering Mathematics, Vol.31, Iss.4, 1997-05, pp. : 337-355

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Abstract

This paper presents a perturbation method for the solution of the electromagnetic and thermal problems of a deformed sphere levitated in an alternating magnetic field. The analytical solutions of the electromagnetic field distribution, the Joule heat generation, the magnetic lifting force and the temperature field are obtained based on a linear perturbation theory. The Maxwell equations are first simplified in terms of the vector potential and then solved by the method of separation of variables. The time-averaged Joule-heat source is calculated and coupled to the Fourier heat-conduction equation. The coupled equation is solved for temperature distributions within the deformed sphere by a combined approach of series expansion and variation of parameters. Both asymptotic and numerical analyses are provided. The total power absorption and temperature field for both single and multiple coils are also discussed.