Heat conduction in anisotropic medium with perfectly conductive thread-like inclusions

The paper presents a novel approach for the analysis of steady-state heat conduction of solids containing perfectly conductive thread-like inhomogeneities. Modelling of a thread-like heat conductive inhomogeneity is reduced to determination of density of heat distributed along a spatial curve, which replaces the inclusion. Corresponding boundary integral equations are obtained for anisotropic solids with thread-like inclusions. Non-integral terms are computed in a closed form. It is shown that, nevertheless the singularity of the equation is 1/r, it is hypersingular, since the kernel is symmetric. Boundary element approach is adopted for solution of the obtained equations. Numerical example is presented for a rectilinear conductive thread, which verifies derived boundary integral equations.

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The present paper is financially supported by the Ministry of Science and Higher Education of Poland (research project No S/WM/4/2017) and realised in Bialystok University of Technology

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Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).