Розроблення математичних моделей теплообміну в сучасних пристроях електронної техніки з теплоактивними зонами канонічної форми

This study examines the heat exchange processes for thermally active and thermally sensitive individual nodes and elements in electronic devices that are subjected to thermal loads in the areas of canonical form. As a result of thermal loads, significant temperature gradients arise. To improve the accuracy of designing electronic devices and for their effective operation, linear and nonlinear mathematical models have been built to analyze their temperature regimes. Based on the stated linear and nonlinear axisymmetric boundary value problems of heat conduction, their analytical and analytical-numerical solutions have been derived. Using these solutions has made it possible to establish the temperature distribution in spatial radial and axial coordinates for given geometric and thermophysical parameters (the chosen graphite has the ability to absorb a significant amount of heat at its thermal conductivity coefficient equal to 372 W/(m∙degree)). To effectively describe canonical heating regions, the theory of generalized functions has been used. A technique for linearizing nonlinear mathematical models has been introduced. As a result, linear second-order differential equations with partial derivatives and a singular right-hand side have been derived. The numerical results reflect the temperature distribution in the medium along the radial and axial coordinates for the given geometric and thermophysical parameters. The number of divisions of the interval (0; r*) was chosen to be 9, which made it possible to obtain numerical values of temperature with an accuracy of 10-6. The resulting numerical values of temperature for the selected materials with a linear temperature dependence of the thermal conductivity coefficient differ from the results obtained for its constant value by 5%. The constructed mathematical models of heat transfer make it possible to analyze spatial isotropic media with respect to their thermal stability