The objective of this work is to introduce and numerically solve a mathematical model for unsteady thermoelectrical behavior of an electric arc electrode. The electrode is composed of several materials and one of them suffers a change of state during operation. Thermoelectric parameters depend on the temperature in each material. The volumetric heat source is the Joule effect. The mathematical model leads to a coupled non-linear system of partial differential equations. The axisymmetry of the domain allows us to simplify the problem when it is written in cylindrical coordinates. We use an implicit method for time discretization and a standard finite element method for space discretization. Numerical results corresponding to the simulation of a real industrial situation are given.
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