Mathematical modeling of the liquid steel entering a container in ingot casting processes
DOI:
https://doi.org/10.32911/as.2021.v14.n2.814Keywords:
mathematical model, energy equation, Peclet's number, cooling processAbstract
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.
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References
Bikerman, J. 1970. Physical Surfaces. New York: Academic Press. <https://www.amazon.com/Physical-Surfaces-J-Bikerman/dp/0124053858>
Brenner, S. 2016. Topics in Numerical Partial Differential Equations and Scientific Computing, New York: Springer. https://www.springer.com/gp/book/10.1007/978-1-4939-6399-7>
Burden R.; Faires J. 2015. Numerical Analysis. Boston: Brooks/Cole.. <https://www.amazon.com/Numerical-Analysis-Richard-L-Burden/dp/1305253663>
Chivers, I.; Sleightholne, J. 2018. Introduction to Programming with Fortran, Suiza: Springer.<https://www.springer.com/gp/book/9783319755014 >
Deitel, P.; Deitel, H. 2010. C++ How to Program, New Jersey: Pearson. <https://www.amazon.com/How-Program-10th-Paul-Deitel/dp/0134448235 >
Donea, J; Huerta, A; Ponthot, J.; Rodriguez-Ferran, A. 2004. Arbitrary Lagrangian-Eulearian Methods. New York: Wiley Online Library. <https://doi.org/10.1002/0470091355.ecm009>
Eaton, W; Bateman, D; Hauberg, S.; Wehbring, R. 2020. GNU Octave - Free Your Numbers. 6ta Edición. Boston: Free Software Foundation. <https://octave.org/octave.pdf >
Langtangen, H.; Linge, S. 2017. Finite Difference Computing with PDEs, Switzerland: Springer.<https://www.springer.com/gp/book/9783319554556 >
Melink, R.; Makrov, R.; Belair, J. 2017. Recent Progress and Modern Challenges in Applied Mathematics, Modeling and Computational Science, Switzerland: Springer Science.<https://www.springer.com/gp/book/9781493969685 >
Savitch, W. 2009. Problem Solving with C++. Boston: Pearson Education Inc. <https://www.amazon.com/Problem-Solving-9th-Walter-Savitch/dp/0133591743>
Tannenhill, J; Anderson, D; Pletcher, R. 1997. Computational Fluid Mechanics and Heat Transfer. Washington, DC: Taylor & Francis.<https://www.amazon.com/Computational-Fluid-Mechanics-Heat-Transfer/dp/B0086HWIKE >
Tomono, H; Kurz, W; Heinemann, W. 1981. «The liquid steel meniscus in molds and its relevance to the surface quality of casting». Metal. Mater. Trans. B 12B. 409-411. <https://doi.org/10.1007/BF02654475>
Vynnycky, M.; Zambrano, M; Cuminato, J. 2015. «On the avoidance of ripple marks on cast metal surfaces». Int. J. Heat Mass Transfer. 86. 43-54. <https://doi.org/10.1016/j.ijheatmasstransfer.2015.02.063>
