# hpfem/esco2012-boa

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 \title{Optimization of the System for Induction Heating of Nonmagnetic Cylindrical Billets in Rotating Magnetic Field Produced by Permanent Magnets} \tocauthor{P. Kus} \author{} \institute{} \maketitle \begin{center} {\large Franti\v sek Mach}\\ West Bohemia University, Pilsen, Czech Republic \\ {\tt fmach@kte.zcu.cz} \\ \vspace{4mm}{\large \underline{Pavel K\r us}}\\ Academy of Science of the Czech Republic, Prague, Czech Republic\\ {\tt pavel.kus@gmail.com} \\ \vspace{4mm}{\large Lubom\' ir Mus\' alek}\\ Czech Technical University, Prague, Czech Republic \\ {\tt musallub@fel.cvut.cz} \\ \vspace{4mm}{\large Pavel Karban, Ivo Dole\v zel}\\ West Bohemia University, Pilsen, Czech Republic \\ {\tt karban@kte.zcu.cz, idolezel@kte.zcu.cz} \end{center} \section*{Abstract} The process of induction heating of cylindrical nonmagnetic billets is modeled. An unmoving billet is placed in rotating magnetic field generated by permanent magnets mounted on a ferromagnetic ring. The ring with the magnets represents an external rotor of the device that is driven by an asynchronous motor by means of a teeth gear. The coupled model of the problem consisting of two partial differential equations describing the distributions of magnetic and temperature fields in the system is solved by a fully adaptive higher-order finite element method. Computations are realized by own code Agros2d developed in our department. The system is then optimized with respect to the thickness of the air gap and angular velocity of rotation. The optimization procedure represents a supplement of the code. The methodology is illustrated by a typical example whose results are discussed. \bibliographystyle{plain} \begin{thebibliography}{10} \bibitem{msdem} {\sc P. Di Barba}. {Multiobjective Shape Design in Electricity and Magnetism}. Lecture Notes in Electrical Engineering, 2010, 9789048130795. \bibitem{etaihabrdcmf} {\sc R. Araneo and R. F. Dughiero and M. Fabbri and M. Forzan and A. Geri and A. Morandi and S. Lupi and P. L. Ribani and G. Veca}. {Electromagnetic and Thermal Analysis of the Induction Heating of Aluminium Billets Rotating in DC Magnetic Field}. COMPEL, 2008, vol. 27, pp. 467-479. \bibitem{ihncbrmfpspm} {\sc P. Karban and F. Mach and I. Dolezel}. {Induction Heating of Nonmagnetic Cylindrical Billets by Rotation in Magnetic Field Produced by Static Permanent Magnets}. Electrical Review, 2010, vol. 86, pp. 53-56. \bibitem{hofemrihncb} {\sc P. Karban and F. Mach and I. Dolezel and J. Barglik}. {Higher-Order Finite Element Modeling of Rotational Induction Heating of Nonferromagnetic Cylindrical Billets}. COMPEL, 2009, vol. 30, pp. 1517-1527. \bibitem{hermes} {\sc P. Solin and et al.}. {Hermes - Higher-Order Modular Finite Element System}. http://hpfem.org. \bibitem{agros} {\sc P. Karban and et al.}. {Agros2D - application for solution of physical fields}. http://agros2d.org. \end{thebibliography}