On the steady-state processes on a plane with a circular inclusion shielded by a two-layer film

The steady-state processes of heat and mass transfer on a plane with a circular inclusion having a boundary in the form of a two-layer film, when the desired potentials inside and outside the circle satisfy Poisson's equation and a generalized matching conditions on the film, are considered. Formulas expressing the potentials of the processes under consideration via the known potentials of similar processes on a homogeneous plane (i.e., without inclusion) are obtained. Examples of solving the problems in finite form are presented.