(untitled) (Eureka Journal of Education & Learning Technologies, 2026)
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.