Existence of solution of a coupled problem arising in the thermoelectrical simulation of electrodes

Bermúdez, Alfredo; Muñoz-Sola, Rafael

doi:10.1090/qam/1724296

Authors: Alfredo Bermúdez and Rafael Muñoz-Sola
Journal: Quart. Appl. Math. 57 (1999), 621-636
MSC: Primary 35Q60; Secondary 78A55, 80A20
DOI: https://doi.org/10.1090/qam/1724296
MathSciNet review: MR1724296
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Abstract: In this paper we prove the existence of a solution to a system of partial differential equations arising from the thermoelectrical modeling of electrodes for electric furnaces. It consists of Maxwell equations coupled with the heat transfer equation through the Joule effect and the fact that thermal conductivity and electrical resistivity depend on temperature. The problem is formulated in cylindrical coordinates to take advantage of its axisymmetry.

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