Mathematical Modeling and Analysis Using Nondimensionalization Technique of the Solidification of a Splat of Variable Section

Juan Francisco Sánchez-Pérez (), Guillermo Jorde-Cerezo, Adrián Fernández-Roiz and José Andrés Moreno-Nicolás
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Juan Francisco Sánchez-Pérez: Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain
Guillermo Jorde-Cerezo: Fundación Centro Tecnológico Miranda de Ebro, 09200 Miranda de Ebro, Spain
Adrián Fernández-Roiz: Fundación Centro Tecnológico Miranda de Ebro, 09200 Miranda de Ebro, Spain
José Andrés Moreno-Nicolás: Department of Mechanical Engineering, Materials and Manufacturing, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain

Mathematics, 2023, vol. 11, issue 14, 1-16

Abstract: In this work, the solidification and cooling process of an irregularly shaped splat is modeled using the network simulation method. The procedure for its implementation, which uses the finite difference method and optimized circuit analysis algorithms, allows the precise incorporation and assessment of the effect of certain conditions in the thermal process, offering its specificity and high performance in numerical simulation. It should be noted, on the one hand, that the geometry used for the simulation has been obtained from experimental splat data visualized using an electron microscope and, on the other hand, that the model implements both the phase change phenomenon and the variability of the material properties with temperature. Finally, the study of the physical behavior of the problem is carried out using the mathematical technique of nondimensionalization, allowing the interpretation of the results obtained by simulation, where the formation of horizontal bars and columns that maintain the structure of the splat while the solidification process is taking place stands out. It is worth highlighting the obtaining, among others, of two monomials. The first relates the phenomenon of radiation to conduction and is equivalent to the Nusselt number with convection, and the second relates the solidification time with the Stefan number.

Keywords: network simulation method; nondimensionalization; ceramic coatings; phase change; differential equations; engineering problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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