Existence of solution of a coupled problem arising in the thermoelectrical simulation of electrodes
Alfredo Bermúdez, Rafael Muñoz‐Sola · Quarterly of Applied Mathematics · 1999
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.