MODELING OF THERMAL PROCESSES: THEORETICAL FOUNDATIONS, NUMERICAL METHODS AND PRACTICAL APPLICATIONS
- Authors
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Komilova Nodira Abdirakhmon qizi
Doctor of Philosophy (PhD) in Pedagogical Sciences, Associate Professor, Almalyk State Technical Institute
Author
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- Keywords:
- Heat conduction, mathematical modeling, finite difference method, finite element method, convection, heat transfer coefficient, energy efficiency, numerical simulation, Fourier equation, Stefan-Boltzmann law.
- Abstract
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This paper presents a comprehensive review of modern mathematical methods for modeling thermal processes and their significance in industrial and scientific research. Differential equations describing heat conduction, convection, and radiation phenomena are introduced, and both analytical and numerical solution methods — the finite difference method (FDM/CFD), the finite element method (FEM), and the Monte Carlo statistical method — are analyzed. Particular attention is given to practical applications in the energy, construction, metallurgy, and chemical industries. The research yields optimized computational algorithms for thermal process modeling, demonstrating 15–30% superiority in accuracy and computational efficiency over existing solutions. The results presented in this article serve as a methodological foundation for new applied research in the fields of thermal engineering and energy.
- References
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- Published
- 2026-05-08
- Issue
- Vol. 2 No. 5 (2026)
- Section
- Articles
- License
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This work is licensed under a Creative Commons Attribution 4.0 International License.
