Heat Conduction in the Infinite Medium With Lines of Discontinuities

Abstract

A mathematical analysis of heat conduction in the infinite region with lines of discontinuities by application of complex variables and the problem of linear relationship is considered. Boundary problems for the plane with straight cuts or inclusions are formulated and solutions are given in closed form. The heat fluxes were found to possess the characteristic inverse square-root singularity in terms of the radial distance from the point of the line of discontinuity, hence approaching high mathematically infinite values at the point itself. It is also shown that the magnitude of the heat flux vector may be obtained from a sectionally holomorphic function without calculating the temperature distribution in the body.