Construction of mathematical models of heat exchange in semi-infinite environments with foreign inclusions

Authors

DOI:

https://doi.org/10.15587/1729-4061.2026.364576

Keywords:

temperature field, thermal conductivity of the material, thermal stability of structures, convective heat transfer, heat flow

Abstract

This study investigates heat transfer processes in isotropic semi-infinite 3D media with foreign inclusions, which are heated by internal sources and heat flow.

As a result of the thermal load during the operation of devices, significant temperature gradients arise. To analyze the temperature regimes and establish the effective operation of these devices, mathematical models for determining temperature fields have been constructed.

Based on the stated boundary value problems of thermal conductivity, their analytical solutions have been derived, which make it possible to obtain the temperature distribution and the behavior of temperature gradients in a heterogeneous medium. 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 thermophysical parameters of heterogeneous semi-infinite 3D media, a symmetric unit function and the Dirac delta function have been used. As a result, second-order differential equations with partial derivatives and singular coefficients have been derived.

The numerical results reflect the temperature distribution in semi-infinite 3D media in spatial coordinates for the given geometric and thermophysical parameters. The numerical values of temperature for the selected half-space material (ceramics VK94-I) and inclusions (silicon, molybdenum) were obtained with an accuracy of 10-6.

The application of the constructed mathematical models of heat transfer contributes to investigating the thermal stability in semi-infinite 3D media with foreign inclusions. Using these models makes it possible to predict temperature regimes in devices, which is a prerequisite for improving their reliability and durability

Author Biographies

Vasyl Havrysh, Lviv Polytechnic National University

Doctor of Technical Sciences, Professor

Department of Software

Svitlana Yatsyshyn, Ukrainian National Forestry University

Candidate of Technical Sciences, Associate Professor

Department of Software Engineering

Halyna Klym, Lviv Polytechnic National University

Doctor of Technical Sciences, Professor

Department of Specialized Computer Systems

Mykhailo Stepaniak, Lviv Polytechnic National University

Candidate of Technical Sciences

Department of Computerized Automatic Systems

Mihaylo Klymiuk, Lviv State University of Life Safety

Candidate of Technical Sciences

Department of Special Rescue Training and Physical Education

References

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Construction of mathematical models of heat exchange in semi-infinite environments with foreign inclusions

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Published

2026-06-23

How to Cite

Havrysh, V., Yatsyshyn, S., Klym, H., Stepaniak, M., & Klymiuk, M. (2026). Construction of mathematical models of heat exchange in semi-infinite environments with foreign inclusions. Eastern-European Journal of Enterprise Technologies, 3(5 (141), 26–35. https://doi.org/10.15587/1729-4061.2026.364576

Issue

Vol. 3 No. 5 (141) (2026): Applied physics

Section

Applied physics

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Copyright (c) 2026 Vasyl Havrysh, Svitlana Yatsyshyn, Halyna Klym, Mykhailo Stepaniak, Mihaylo Klymiuk

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