Mathematical modeling of the liquid steel entering a container in ingot casting processes (Aporte Santiaguino, 2021)
In the present work, a mathematical model is developed which involves the equations of fluid mechanics and the energy equation to determine the temperature field of the liquid steel that enters a container to solidify, a situation commonly found in production processes of steel today. Using mathematical techniques, a simplified equation of the energy equation is obtained in which a non-dimensional parameter Pe, the Peclet number, allows to evaluate the transport of the heat by convection to the transmission by diffusion occurred in the mold that contains liquid steel. Using finite differences method, the mathematical model formulated is solved numerically to visualize the cooling process of the liquid steel, from the beginning until the solidification process starts. Likewise, the numerical computations are carried out using GNU-Octave, which is a platform to the scientific programming which allowed the visualization of the results obtained in different phases of the cooling process.
Keywords: mathematical model, energy equation, Peclet's number, cooling process