Thermal behavior of a conductor submitted to skin effect

Induction furnaces used for metallurgy operate with high power and high frequency currents. Under these conditions the current density is not unvarying in a cross-section of the feeding cable, but increases powerfully towards the periphery (skin effect). Without sufficient cooling high temperatures and melting at local level can be expected. Moreover, as these cables are near the furnace, they are exposed to high outside temperatures. Despite the drop in its electrical conductivity at high temperatures, tungsten is compared with copper because it has the highest melting point and the highest critical frequency. These features must be taken into account in the supply plan: this article provides a quick procedure, by using a sub-program which is available in many computer systems, in order to assess the temperatures and energy losses corresponding to different values for the physical parameters. From a practical point of view it seems that skin effect does not cause overheating locally, but requires a much greater degree of cooling, so the choice between copper and tungsten (or any conductive alloy) must take two elements into consideration: the high temperature caused by the environment and the cooling device. The financial impact does not appear to be great.