Abstract
The article analyzes the Mathematical Model of The Self-Baking Electrode which is defined as basic. Its advantages and disadvantages are determined. Criterias for creating more advanced mathematical model for equalizing the thermal field of the Electrode are proposed.
 The problem of calculating the thermal field is solved by the the method of elementary heat balances of electrode. For this goal the simulated area is divided into annular (cylindrical) elements along the radius and height of the electrode.The calculation of the temperature field of the electrode is carried out in two stages: I – with boundary conditions and currents for the parts of the electrode facing to the center of the smelting furnace; II – with boundary conditions and currents for the parts of the electrode facing to the lining. 
 The mathematical model takes into account an effect of the ribs and the hood on the distribution of electric current and Joule’s Heat over the cross section of the Electrode. In case heating ferromagnetic materials under impact of an electromagnetic field, the magnetic permeability at first decreases relatively slowly, and then droping down sharply as a certain temperature (Curie Point) is reached. The material loses its magnetic properties completely and goes into into a paramagnetic state.
 The value of the electrode current changes according to the graph from the starting value to the working value and then remains constant. The current density of the electrode along the radius is unequal due to the action of the surface effect, as well as due to existence of a metal hood and ribs, the electrical conductivity of which is higher than conductivity of special carbon paste.
 The goal of the work is to create modern mathematical model of the secondary current network of electric smelting furnace which could improve baking conditions of the Electrode and to reach the state of its temperature field to equable. This would create a stable mode of operation of the furnace.The paper analyzes the main features of the mathematical model of the secondary network of the smelting furnace, identifies the stages of development and formulates the main assumptionssimplifications that could be accepted wile creating this model.
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