<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Heat Conduction in Anisotropic Medium with Perfectly Conductive Thread-Like Inclusions

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The paper presents a novel approach for the analysis of steady-state heat conduction of solids containing perfectly conductive thread-like inhomogeneities....

Heat Conduction in Anisotropic Medium with Perfectly Conductive Thread-Like Inclusions

Published Online: Jan 30, 2020

Page range: 251 - 254

Received: May 21, 2019

Accepted: Jan 10, 2020

DOI: https://doi.org/10.2478/ama-2019-0034

Keywords
thread-like inclusion, steady-state heat conduction, anisotropy, boundary integral equation, hypersingular

© 2019 Heorhiy Sulym et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Heat Conduction in Anisotropic Medium with Perfectly Conductive Thread-Like Inclusions

Published Online: Jan 30, 2020

Page range: 251 - 254

Received: May 21, 2019

Accepted: Jan 10, 2020

DOI: https://doi.org/10.2478/ama-2019-0034

Keywordsthread-like inclusion, steady-state heat conduction, anisotropy, boundary integral equation, hypersingular

© 2019 Heorhiy Sulym et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
thread-like inclusion, steady-state heat conduction, anisotropy, boundary integral equation, hypersingular