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Shock and Vibration
Volume 2, Issue 3, Pages 219-225

Effective Method for Analysis of Electrothermally Coupled Fields

Jacek Korytkowski and Stanisław Wincenciak

Warsaw University of Technology, Electrical Engineering Department, Institute of the Theory of Electrical Engineering and Electrical Measurements, 00-662 Warsaw, Koszykowa 75, Poland

Received 17 June 1994; Accepted 6 November 1994

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An effective method is presented for solving a nonlinear system of partial differential equations that describe the time-dependent electrothermally coupled fields for passage of constant electric current in a three-dimensional conductive medium. A numerical model of this physical phenomenon was obtained by the finite element method, which takes into account the temperature-dependent characteristics describing the material parameters and conditions of heat transmission outside of the analyzed objects. These characteristics and conditions make the problem strongly nonlinear. The solution uses the Newton-Raphson method with the appropriate procedure for determining the Jacobian matrix elements. The main idea of the proposed method is the use of an automatic time step selection algorithm to solve heat conduction equations. The influence of the assumed accuracy value on the final result of the nonlinear calculation is discussed. The theoretical results were confirmed by the numerical experiments performed with selected physical objects.