Axisymmetric Heat Conduction in a Cracked Layer Subjected to Prescribed Temperatures

This paper presents an analysis of an axisymmetric heat conduction problem in a layer with circular heat sources on its external surfaces, maintaining constant temperatures. Additionally, the layer contains a circular crack along its middle plane, either internally or externally, leading to a mixed boundary value problem. In this study, dual integral equations are derived using Hankel’s transform technique. In contrast to the conventional approach that relies on Fredholm’s equations, these dual integral equations are directly reduced to an infinite set of simultaneous equations. The investigation subsequently provides closed-form expressions involving special functions for the thermal fields and heat flux intensity factor. Moreover, the solution for the case of a half-space medium is obtained as a limiting case of this study. The accuracy and validity of the present approach are also confirmed through comparison with numerical simulations. Sets of plots are provided to analyze the influence of the crack, surface radius of the applied temperatures, and the layer thickness on various physical quantities.