A new boundary element formulation of coupled electromagnetic and thermal skin effect problems for non-harmonic regimes of current passage

A new economic technique for the calculation of Joule heating in the skin layer of arbitrarily shaped parallel conductors carrying transient current is presented. The technique is based on the BIE-BLA (boundary integral equation-boundary layer approximation) formulation that generalizes the BIE-IBC (boundary integral equation-impedance boundary condition) formulations for time-harmonic problems to transient problems. The final integral equations are formulated in such a way that new computational complications do not arise as compared with solving the problem using well-known perfect conductor limit. The technique is applicable to non-linear materials as well as linear materials. For the linear material situation, an analytical solution of the surface temperature of the conductor heated by a step current pulse is obtained. A numerical example is included to illustrate the method