Construction of mathematical models of heat exchange in electronic devices with semi-through foreign elements
DOI:
https://doi.org/10.15587/1729-4061.2026.357609Keywords:
temperature field, thermal conductivity of the material, thermal resistance of structures, heat transfer, semi-through foreign elementsAbstract
This study investigates heat exchange processes in isotropic spatial environments with foreign semi-through elements subjected to external and internal thermal loads.
Significant temperature gradients arise as a result of the thermal load. To establish and analyze temperature regimes for effective operation of electronic devices, mathematical models for determining temperature fields have been constructed.
Based on the formulated boundary value problems of thermal conductivity, their analytical and numerical solutions have been defined. Using these solutions, numerical calculations of the temperature distribution in spatial coordinates for given geometric and thermophysical parameters have been performed.
For an effective description of the thermal conductivity coefficient for inhomogeneous spatial media, asymmetric unit functions were used. A technique for segment-constant approximation of temperature as a function of spatial coordinates on the surfaces of foreign elements has been introduced. As a result, second-order differential equations with partial derivatives and discontinuous and singular coefficients have been derived.
The numerical results reflect temperature distribution in the media in spatial coordinates for the given geometric and thermophysical parameters. The number of partitions of the intervals (0; h), (–H; H), (0; R) was chosen to be equal to 9. That has made it possible to obtain numerical values of temperature with an accuracy of 10–6. The constructed mathematical models of heat transfer make it possible to analyze spatial isotropic media with foreign through-going elements in terms of their thermal stability
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Copyright (c) 2026 Vasyl Havrysh, Svitlana Yatsyshyn, Lubov Kolyasa, Mykhailo Stepaniak, Andrii Kapustianskyi
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