An estimator for equivalent properties of a bundle of conductors using the inverse problem method

In this paper, a method is introduced to calculate the equivalent electromagnetic and thermal properties of nonhomogeneous materials. The study is in large part applied to a bundle of conductors. For a filling rate, the conductors are distributed inside a cylindrical geometry using a Monte-Carlo random algorithm. Electromagnetic and thermal equations are solved in this nonhomogeneous material and the total power, magnetic field and temperature distribution are calculated. Supposing an equivalent homogeneous cylinder, the inverse problem methodology is used to calculate the electromagnetic and thermal properties of the equivalent material which give the same power, mean magnetic field or mean temperature distribution. The validity of these hypotheses are then discussed.