Математичне моделювання процесу нестаціонарної теплопровідності крізь стінку

M. M. Biliaiev; V. V. Biliaieva; P. S. Kirichenko; V. A. Kozachyna; V. M. Poltoratska

doi:10.15802/stp2025/337686

Authors

M. M. Biliaiev Ukrainian State University of Science and Technologies, SEI DIIT, Ukraine https://orcid.org/0000-0002-1531-7882
V. V. Biliaieva Ukrainian State University of Science and technologies, SEI DMetl, Ukraine https://orcid.org/0000-0003-2399-3124
P. S. Kirichenko Kryvyi Rih National University, Ukraine https://orcid.org/0000-0002-0793-9593
V. A. Kozachyna Ukrainian State University of Science and Technologies, SEI DIIT, Ukraine https://orcid.org/0000-0002-6894-5532
V. M. Poltoratska Ukrainian State University of Science and Technologies, SEI PSACEA, Ukraine https://orcid.org/0000-0002-6244-8439

DOI:

https://doi.org/10.15802/stp2025/337686

Keywords:

occupational safety, industrial site, mathematical modeling, heat transfer, fire, temperature field, protective barrier

Abstract

Purpose. Extreme situations at industrial facilities often lead to fires, in particular, fires occur in the event of drone attacks on oil storage facilities. In such cases, a significant amount of chemically hazardous substances (fuel combustion products) are released into the air, posing a risk of thermal injury to workers. Various means and structures are used to reduce the risk of thermal injury. When designing protective structures, it is necessary to determine in advance their effectiveness and the time of possible destruction. This requires the development and use of specialized mathematical models. This work is devoted to the development of numerical models that allow predicting thermal fields at an industrial site in case of fire and assessing the risk of destruction of a protective wall (barrier). Methodology. To numerically solve aerodynamic problems (determining the wind speed field), calculate areas of thermal pollution of the air at an industrial site, and determine the dynamics of temperature changes inside a protective barrier (wall), we use fundamental models of continuum mechanics. Finite difference schemes are used for the numerical solution of simulation equations. Findings. A computer program has been developed that makes it possible to solve a «coupled» problem of determining the zone of thermal pollution of air at an industrial site and the dynamics of heating of a protective barrier (wall). Using the proposed numerical model and computer program, it is possible to solve the problem of thermal conductivity and heat transfer in real time. Originality. A fast-calculation numerical model is presented for estimating the time of destruction of a protective barrier at an industrial site where a fire occurs. The analysis of thermal fields at an industrial site and inside the protective barrier was carried out by numerical integration of a multivariable heat transfer and heat conduction equation. The aerodynamics problem was solved based on a potential motion model. These numerical models require little computer time for practical implementation. Practical value. The proposed numerical models can be used for a preliminary assessment of the temperature field inside the protective barrier to determine its effectiveness in terms of protecting areas from thermal pollution at an industrial site. This info can be useful at the preliminary design stage of protective structures.

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