Nonlinear Boundary-Value Problem of Heat Conduction for a Layered Plate with Inclusion

Abstract

We consider a nonlinear boundary-value problem of heat conduction for an isotropic infinite heat-sensitive layered plate with heat-insulated faces containing a foreign through thermally active inclusion. By using the proposed transformation, we perform partial linearization of the initial heat-conduction equation. As a result of a piecewise-linear approximation of temperatures on the boundary surfaces of the foreign layers and the inclusion, the equation is completely linearized. We find an analytic-numerical solution of this equation with boundary conditions of the second kind in order to determine the introduced function with the use of the Fourier integral transformation. The computational formulas for the unknown values of temperature are presented in the case of a linear temperature dependence of the heat-conduction coefficients of structural materials for the two-layer plates. The numerical analysis is performed for a single-layer plate containing a through thermally active inclusion (the material of the plate is VK94-I ceramic and the material of the inclusion is silver).