A fixed point approach to stationary heat transfer in electric cables

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 pro...

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Main Authors:	Karl Dvorsky, Joachim Gwinner, Hans-Dieter Liess
Format:	Article
Language:	English
Published:	Vilnius Gediminas Technical University 2011-06-01
Series:	Mathematical Modelling and Analysis
Subjects:	Heat transfer problem nonlinear boundary integral equations contractive mapping iterative method electric cables
Online Access:	https://journals.vgtu.lt/index.php/MMA/article/view/5530

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spelling	doaj-0a8b6c6afe474cedbb4cc55da38994cf2021-07-02T07:04:48ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102011-06-0116210.3846/13926292.2011.580436A fixed point approach to stationary heat transfer in electric cablesKarl Dvorsky0Joachim Gwinner1Hans-Dieter Liess2Department of Aerospace Engineering, Institute of Mathematics, Universität der Bundeswehr München, D-85577 Neubiberg, GermanyDepartment of Aerospace Engineering, Institute of Mathematics, Universität der Bundeswehr München, D-85577 Neubiberg, GermanyDepartment of Electrical Engineering and Information Technology, Universität der Bundeswehr München, D-85577 Neubiberg, Germany 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. https://journals.vgtu.lt/index.php/MMA/article/view/5530Heat transfer problemnonlinear boundary integral equationscontractive mappingiterative methodelectric cables
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Karl Dvorsky Joachim Gwinner Hans-Dieter Liess
spellingShingle	Karl Dvorsky Joachim Gwinner Hans-Dieter Liess A fixed point approach to stationary heat transfer in electric cables Mathematical Modelling and Analysis Heat transfer problem nonlinear boundary integral equations contractive mapping iterative method electric cables
author_facet	Karl Dvorsky Joachim Gwinner Hans-Dieter Liess
author_sort	Karl Dvorsky
title	A fixed point approach to stationary heat transfer in electric cables
title_short	A fixed point approach to stationary heat transfer in electric cables
title_full	A fixed point approach to stationary heat transfer in electric cables
title_fullStr	A fixed point approach to stationary heat transfer in electric cables
title_full_unstemmed	A fixed point approach to stationary heat transfer in electric cables
title_sort	fixed point approach to stationary heat transfer in electric cables
publisher	Vilnius Gediminas Technical University
series	Mathematical Modelling and Analysis
issn	1392-6292 1648-3510
publishDate	2011-06-01
description	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.
topic	Heat transfer problem nonlinear boundary integral equations contractive mapping iterative method electric cables
url	https://journals.vgtu.lt/index.php/MMA/article/view/5530
work_keys_str_mv	AT karldvorsky afixedpointapproachtostationaryheattransferinelectriccables AT joachimgwinner afixedpointapproachtostationaryheattransferinelectriccables AT hansdieterliess afixedpointapproachtostationaryheattransferinelectriccables AT karldvorsky fixedpointapproachtostationaryheattransferinelectriccables AT joachimgwinner fixedpointapproachtostationaryheattransferinelectriccables AT hansdieterliess fixedpointapproachtostationaryheattransferinelectriccables
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A fixed point approach to stationary heat transfer in electric cables

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