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Joule heating and thermistor problems with mixed boundary conditions

Joule heating and thermistor problems with mixed boundary conditions July, 1994 ACTA MATHEMATICAE APPLICATAE SINICA Vol.10 No.3 Study Bulletin JOULE HEATING AND THERMISTOR PROBLEMS WITH MIXED BOUNDARY CONDITIONS* CHEN QIHONG (~ ~ ~) ( Sur.l~u Institute of Urban Cor~truc$ion and Environmental Pro~ection, Suzhou 215008, China) 1. Introduction Joule heating is generated by the resistance of materials to electric current and is present in any electric conductor. Let u be the absolute temperature and ¢ the electric potential in a solid electric conductor represented by a bounded domain f~ of R 3. Under steady conditions, the Joule heating problem consists of the following nonlinear elliptic system V-(a(u)V¢) ---- O, in f~, (1.1) - v. (k(~)v~) -- ,~(~,)lV¢l 2, in fl (1.2) with some suitable boundary conditions, where (r(u) and k(u) are respectively the electrical and thermal conductivities which we suppose to be given positive function of the tempera- ture. When or(u) decreases markedly in a narrow temperature range, the device is called a thermistor. In this case, Equation (1.1) may become degenerate. The Joule heating and thermistor problems arise in many industrial applications and have called some attention recently. (For the physical background refer to [1], [2] and the references therein.) From the mathematical point of view the interest http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Joule heating and thermistor problems with mixed boundary conditions

Acta Mathematicae Applicatae Sinica , Volume 10 (3) – Jul 13, 2005

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Publisher
Springer Journals
Copyright
Copyright © 1994 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006863
Publisher site
See Article on Publisher Site

Abstract

July, 1994 ACTA MATHEMATICAE APPLICATAE SINICA Vol.10 No.3 Study Bulletin JOULE HEATING AND THERMISTOR PROBLEMS WITH MIXED BOUNDARY CONDITIONS* CHEN QIHONG (~ ~ ~) ( Sur.l~u Institute of Urban Cor~truc$ion and Environmental Pro~ection, Suzhou 215008, China) 1. Introduction Joule heating is generated by the resistance of materials to electric current and is present in any electric conductor. Let u be the absolute temperature and ¢ the electric potential in a solid electric conductor represented by a bounded domain f~ of R 3. Under steady conditions, the Joule heating problem consists of the following nonlinear elliptic system V-(a(u)V¢) ---- O, in f~, (1.1) - v. (k(~)v~) -- ,~(~,)lV¢l 2, in fl (1.2) with some suitable boundary conditions, where (r(u) and k(u) are respectively the electrical and thermal conductivities which we suppose to be given positive function of the tempera- ture. When or(u) decreases markedly in a narrow temperature range, the device is called a thermistor. In this case, Equation (1.1) may become degenerate. The Joule heating and thermistor problems arise in many industrial applications and have called some attention recently. (For the physical background refer to [1], [2] and the references therein.) From the mathematical point of view the interest

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

References