Solution of the Problem of Heat Conduction for the Transversely Isotropic Piecewise-Homogeneous Space with Two Circular Inclusions

Abstract

The nonaxisymmetric problem of heat conduction for a piecewise-homogeneous transversely isotropic space with two (thermally active and thermally insulated) internal inclusions located parallel to the plane of conjugation of two different transversely isotropic half spaces is reduced to a system of two two-dimensional singular integral equations. The solution of this system is constructed in the form of series in Jacobi polynomials. As a result, we obtain the dependences of the temperature distribution on the thermophysical properties of materials and on the distances between the inclusions and the interface of the half spaces. The quantitative and qualitative specific features of the temperature field in the neighborhood of inclusions are analyzed.