Construction of mathematical models of thermal conductivity for modern electronic devices with elements of a layered structure

Authors

DOI:

https://doi.org/10.15587/1729-4061.2024.309346

Keywords:

temperature field, thermal conductivity of material, thermal resistance of structures, thermosensitive material, thermally active surface

Abstract

This paper considers a heat conduction process for isotropic layered media with internal thermal heating. As a result of the heterogeneity of environments, significant temperature gradients arise as a result of the thermal load. In order to establish the temperature regimes for the effective operation of electronic devices, linear and non-linear mathematical models for determining the temperature field have been constructed, which would make it possible to further analyze the temperature regimes in these heat-active environments. The coefficient of thermal conductivity for the above structures was represented as a whole using asymmetric unit functions. As a result, the conditions of ideal thermal contact were automatically fulfilled on the surfaces of the conjugation of the layers. This leads to solving one heat conduction equation with discontinuous and singular coefficients and boundary conditions at the boundary surfaces of the medium. For linearization of nonlinear boundary value problems, linearizing functions were introduced. Analytical solutions to both linear and nonlinear boundary value problems were derived in a closed form. For heat-sensitive environments, as an example, the linear dependence of the coefficient of thermal conductivity of structural materials on temperature, which is often observed when solving many practical problems, was chosen. As a result, analytical relations for determining the temperature distribution in these environments were obtained. Based on this, a numerical experiment was performed, and it was geometrically represented depending on the spatial coordinates. This proves that the constructed linear and nonlinear mathematical models testify to their adequacy to the real physical process. They make it possible to analyze heat-active media regarding their thermal resistance. As a result, it becomes possible to increase it and protect it from overheating, which can cause the destruction of not only individual nodes and their elements but also the entire structure

Author Biographies

Vasyl Havrysh, Lviv Polytechnic National University

Doctor of Technical Sciences, Professor

Department of Software

Elvira Dzhumelia, Lviv Polytechnic National University

PhD

Department of Software

Stepan Kachan, Lviv Polytechnic National University

PhD, Associate Professor

Department of Civil Safety

Viktoria Maikher, Lviv Polytechnic National University

PhD

Department of Software

Ihor Rabiichuk, Lviv Polytechnic National University

PhD Student

Department of Software

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Construction of mathematical models of thermal conductivity for modern electronic devices with elements of a layered structure

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Published

2024-08-28

How to Cite

Havrysh, V., Dzhumelia, E., Kachan, S., Maikher, V., & Rabiichuk, I. (2024). Construction of mathematical models of thermal conductivity for modern electronic devices with elements of a layered structure . Eastern-European Journal of Enterprise Technologies, 4(5 (130), 34–44. https://doi.org/10.15587/1729-4061.2024.309346

Issue

Vol. 4 No. 5 (130) (2024): Applied physics

Section

Applied physics

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Copyright (c) 2024 Vasyl Havrysh, Elvira Dzhumelia, Stepan Kachan, Viktoria Maikher, Ihor Rabiichuk

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