A fixed point approach to stationary heat transfer in electric cables
Abstract
In this paper we present a novel procedure for the determination of temperature in electric conductors. A Helmholtz-to-Poisson estimate is proved, that justifies to restrict the temperature dependence of the electrical resistivity to the conductor boundary. Hence we obtain a nonlinear potential problem for the relevant boundary temperatures, where the temperature dependence of the heat transfer coefficient is fully regarded. Using boundary integral operators, we represent the unknowns as the fixed point of a contraction. Finally a benchmark example is given in the rotationally symmetric case.
Keywords:
Heat transfer problem, nonlinear boundary integral equations, contractive mapping, iterative method, electric cablesHow to Cite
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Copyright (c) 2011 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2011 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.