Investigation of Temperature Fields in a Heat-Sensitive Layer with Through Inclusion

Abstract

We consider a nonlinear axially symmetric boundary-value problem of heat conduction for a heat-sensitive isotropic layer with through foreign cylindrical inclusion. A heat flux is concentrated on one of the boundary surfaces of this inclusion. By using an introduced linearizing function, we perform partial linearization of the initial problem. As a result of piecewise linear approximation of temperature on the boundary surface of the inclusion, the boundary-value problem becomes completely linearized. With the help of the Hankel integral transformation, we obtain a numerical-analytic solution of the problem of determination of the linearizing function. We also present the computational formulas for temperature in the case of linear temperature dependence of the coefficients of thermal conductivity of structural materials. We also compute and analyze the temperature field in the “layer–inclusion” structure (the materials of the layer and inclusion are VK94-I ceramic and silver, respectively).