Mathematical Models to Determine Temperature Fields in Heterogeneous Elements of Digital Devices with Thermal Sensitivity Taken into Account

Linear and nonlinear mathematical models for determining a temperature field and subsequently analysis of temperature distribution in isotropic spatial media with semi-through foreign inclusions subjected to internal and external thermal loads are considered. For this purpose, the heat transfer coefficient for such structures is considered as a single unit using asymmetric unit functions, which allows considering the boundary value problems of heat transfer with one linear and nonlinear differential equations of heat transfer with discontinuous and singular coefficients as well as linear and nonlinear boundary conditions on the boundary surfaces of the media. The analytic expressions in the form of quadratic equations were obtained for determining the temperature distribution in a thermally sensitive layer with a foreign semi-through inclusion under external heating by a thermal flux. A numerical analysis of the temperature as a function of spatial coordinates for certain geometric and thermophysical parameters is performed. The theoretical studies are applied for BK94-I ceramic with the silver inclusion.