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Most industrial furnaces have a furnace shell. Although these effects are significant and well-known, they are often neglected in electrode models which typically concentrate on a single electrode. The proximity effects typically yield an asymmetric current density in the electrodes.
#Nist comsol 5.3 skin
In addition to the skin effect, there are also considerable proximity effects caused by eddy currents opposing the magnetic field produced by the currents in the neighboring electrodes. The current density distribution in an electrode with skin effect is found by solving Maxwell’s equations, and for the typical case with vertical currents and cylinder geometry, the current density is axisymmetric and given in terms of Bessel functions. The skin effect is caused by eddy currents that are induced by the changing magnetic field produced by the current. Although direct current (DC) furnaces can be found in the industry, most units use AC current, and in AC electrodes, there is considerable concentration of currents close to the surface the well-known skin effect. The electrodes are made of electrically conductive graphite or baked carbon material, and their main function is to carry the electric currents needed for powering the chemical reactions of the process. Also, for designing the furnace and for understanding its process, the current-carrying capabilities and sizing of the electrode play an important role. Detailed understanding of current densities, thermal conditions and mechanical stresses is needed to address electrode problems such as electrode breakages and electrode consumption. Correct and stable operation of the electrodes is of crucial importance for successful and cost-effective operation of the furnace. Typically, three-phase alternating current (AC) circuits using three or more electrodes are used, operating at the grid frequency of 50 or 60 Hz. Examples of such units are slag resistance furnaces and electric arc furnaces, used in the production of steel, ferroalloys, calcium carbide and silicon.
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In many metal-producing units, the energy needed for the primary reactions are delivered by electric currents through large electrodes. In 3D, the shell currents are significantly smaller than what are predicted by the 2D models, but they are sufficiently strong to cause a significant correction of the electrode current density. Finally, the 2D models have been compared with three-dimensional (3D) case studies of large industrial furnaces. This electrode-shell proximity effect competes with the electrode-electrode proximity effect.
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However, strong shell currents may have a significant impact on the current distribution within the electrodes. The analytical models are accurate when induced shell currents can be disregarded. These models are compared to numerical studies including distributed electrodes and shell currents. The third model shows how the strength of the induced shell currents will depend on electrode position and furnace size. The first two models show how the skin and proximity effects depend on electrode material properties and size, and the distance between the electrodes. The models cover three different cases: one electrode only, three electrodes where two are approximated by line currents, and induced shell currents where all electrodes are approximated by line currents. A review of two-dimensional (2D) analytical models of skin and proximity effects in large industrial furnaces with three electrodes arranged in an equilateral triangle is given.