Abstract: In many industrial processes the electric and magnetic properties of a conducting medium can vary with respect to geometrical coordinates. Examples include surface hardening, decarbonization and other applications. Mathematical models for the analysis of electrically conducting media with varying electric conductivity and magnetic permeability have to be developed in order to take into account variability of the properties of the medium.
Analytical solutions of eddy current problems for electrically conducting media with constant properties are well-known in the literature. The focus in the present talk is on the cases where the magnetic permeability and electric conductivity of the medium depend on one geometrical coordinate (vertical coordinate in the case of a multilayer planar medium or radial coordinate in the case a mutlilayer tube). Examples of spherical geometry will be discussed as well.
There are at least two basic methods that are used to model eddy current problems for media with varying properties. First, one can use the solutions for multilayer medim with constant properties assuming that the change in electric conductivity and/or magnetic permeability is represented by piecewise constant functions. However, rapid changes in the properties of each layer may require to use many layers. Second, analytical solutions can be constructed by selecting a relatively simple one- or two-parameter families of electic conductivity and magnetic permeability profiles (in the form of an exponential or power function). Experimental data confirm that such approximations are reasonable.The solution to the Maxwell’s equations in these cases can be obtained in closed form in terms of known special functions. Examples of using the second approach will be discussed.

Brief Biography of the Speaker:
Andrei Kolyshkin received his undergraduate degree in Applied Mathematics in 1976 at the Riga Technical University. In 1981 he received a Ph.D in differential equations and mathematical physics at the University of St. Petersburg (Russia). Andrei Kolyshkin is currently a full professor at the Department of Engineering Mathematics at the Riga Technical University. His current research interests include investigation of stability problems in fluid mechanics with applications to open- channel flows, transient flows in hydraulic systems and mathematical models for eddy current testing. He is the co-author of three monographs published by Academic Press and CRM. Andrei Kolyshkin has participated in more than 40 international conferences and has published more than 70 papers in refereed journals since 1980. As a visiting professor and visiting researcher he spent a few years at the University of Ottawa and Hong Kong University of Science and Technology.