Heat-Distribution Approximation of Cylindrical Wire Carrying an Alternating Current

This article presents a new approach for calculating the heat distribution of a cylindrical wire carrying an alternating current. It is an approximation method that uses the skin-depth factor to distribute the heat flow into two different directions. The main objective of this method is to develop a relatively simple heat equation to calculate the temperature in cylindrical wire without using Basel functions. First, a Fourier heat equation for direct current is shown and compared with 2D FEM simulation results. Then the  approximation formula will be derived from the Fourier heat equation for the case of alternating current (AC). A 2D FEM simulation is also performed for this case to validate the results of the approximation formula. The results show that the approximation formula is very suitable for most applications.