Abstract
The primary objective of this study is to develop a physical and mathematical model of melt hydrodynamics to enhance the understanding of the structural and physical properties of molten systems. The mathematical modeling of hydrodynamic processes is based on the Navier-Stokes equations. To obtain a priori estimates, the Galerkin approach was applied to transfer the limit, enabling the numerical solution of the Navier-Stokes equations with appropriate boundary conditions. A mathematical model describing the incompressible melt motion within a limited area was developed. Additionally, a computer program was created for the numerical solution of the hydrodynamic equations. An algorithm was also developed to construct the distribution of flow rates in molten systems based on numerical experiments. A physical and mathematical model of the incompressible melt motion was specifically constructed for the continuous rolling lines of «Kazakhmys Corporation» LLP used for copper rods. During the hot continuous rolling of copper alloys, the issue of copper sticking to the chute significantly impacts the quality of the final copper products. This study addresses the problem of copper sticking during the hot rolling process by investigating key technologies aimed at improving the production line process of copper rods.