An exact analytical solution of an R-linear conjugation problem for a n-phased concentric circular heterogeneous structure

A 2-D potential steady-state field in an infinite homogeneous matrix with one (n−1)-phased concentric annular inclusion is investigated. It is supposed that the power field in this structure is generated by an arbitrary multipole at infinity. The corresponding boundary value problem is reduced to an equivalent functional equation, which is explicitly solved. Effective resistivities of inclusion and energy dissipation into it are analytically evaluated. Equipotential lines and streamlines are presented.