volume | PIER Journals

Abstract

This paper presents a novel contribution for the analysis of skin effect phenomena in inhomogeneous tubular conductors. For homogeneous tubular geometries the skin effect diffusion equation has an analytical solution described by a combination of Bessel functions, but, when the conductivity and magnetic permeability of the tubular conductor arbitrarily depend on the radial coordinate an analytical solution cannot be found. However, this work shows that closed form solutions for the electromagnetic field and conductor internal impedance do exist, provided that a specific type of radial variation of medium parameters is considered --- tubular structures like these are coined here Euler-Cauchy Structures (ECS). Analytic and computation results concerning general and particular ECS are presented, validated, and discussed. Besides its intrinsic theoretical importance, the simple closed form solutions that we have found can be of interest as benchmark tools for testing the accuracy and performance of EM field software solvers.

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Prof. Jose Antonio Marinho Brandao Faria