  This paper considers the problem of heat transfer in a composite ceramic
material where the structural elements are bonded to the matrix via a thin heat
resistant adhesive layer. The layer has the form of a circular ring or close to
it. Using an asymptotic approach, the interphase is modeled by an infinitesimal
imperfect interface, preserving the main features of the temperature fields
around the interphase, and allowing a significant simplification where FEM
analysis is concerned. The nonlinear transmission conditions that accompany
such an imperfect interface are evaluated, and their accuracy is verified by
means of dedicated analytical examples as well as carefully designed FEM
simulations. The interphases of various geometries are analysed, with an
emphasis on the influence of the curvature of their boundaries on the accuracy
of the evaluated conditions. Numerical results demonstrate the benefits of the
approach and its limitations.
