Effective boundary conditions for a thin curved layer imbedded in a homogeneous medium

Effective impedance boundary conditions for in a thin cylindrical curved layer imbedded in a homogeneous medium in conditions of different contacts are considered. Explicit forms of the second-order approximate boundary conditions are derived for a two-dimensional case. The methodology of investigation is based on the method of matched asymptotic expansions with the thickness-to-length ratio as the perturbation parameter.