Construction of mathematical models of heat exchange in modern electronic devices with thermal active zones of canonical form

Authors

DOI:

https://doi.org/10.15587/1729-4061.2025.346809

Keywords:

temperature field, thermal conductivity of material, thermal resistance of structures, thermally sensitive material, canonical region

Abstract

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

Author Biographies

Vasyl Havrysh, Lviv Polytechnic National University

Doctor of Technical Sciences, Professor

Department of Software

Svitlana Yatsyshyn, Ukrainian National Forestry University

PhD

Department of Software Engineering

Mykhailo Semerak, Lviv Polytechnic National University

Doctor of Technical Sciences, Professor

Department of Heat Engineering and Thermal and Nuclear Power Plants

Mihaylo Klymiuk, Lviv State University of Life Safety

PhD, Deputy Head of the Institute of Postgraduate Education

Fedir Honchar, Lviv Polytechnic National University

PhD

Department of General Physics

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Construction of mathematical models of heat exchange in modern electronic devices with thermal active zones of canonical form

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Published

2025-12-23

How to Cite

Havrysh, V., Yatsyshyn, S., Semerak, M., Klymiuk, M., & Honchar, F. (2025). Construction of mathematical models of heat exchange in modern electronic devices with thermal active zones of canonical form. Eastern-European Journal of Enterprise Technologies, 6(5 (138), 24–33. https://doi.org/10.15587/1729-4061.2025.346809

Issue

Vol. 6 No. 5 (138) (2025): Applied physics

Section

Applied physics

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Copyright (c) 2025 Vasyl Havrysh, Svitlana Yatsyshyn, Mykhailo Semerak, Mihaylo Klymiuk, Fedir Honchar

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