Modelling Temperature Field in Spatial Thermo-Sensitive Elements of Electronic Devices With Local Thermal Heating

A non-linear mathematical model for the determination of the temperature field, and subsequently for the analysis of temperature regimes in an isotropic spatially heat-sensitive heterogeneous environment, which is subjected to an external heat load, has been developed. This model was linearized using the Kirchhoff transformation, as a result of which the Fourier integral transformation method was applied to the obtained linear boundary value problem and an analytical solution was obtained that determines the Kirchhoff linearizing function. As an example, the linear dependence of the coefficient of thermal conductivity of structural materials of the structure on temperature, which is often used in many practical problems, is chosen. As a result, an analytical relation in the form of a nonlinear equation was obtained for determining the temperature distribution in a thermosensitive half-space with a foreign inclusion during external local heating. Numerical analysis of temperature behavior as a function of spatial coordinates for given values of geometric and thermophysical parameters was performed.