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

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.

Deduction of the Dimensionless Groups and Type Curves of Temperature Profiles in Two-Layer Soils with Water Flow at Depth

“…Once the dimensional variables of the governing equation have been replaced by their corresponding dimensionless variables, and the terms of the equation have been simplified (eliminating the derivative factors of these terms), the dimensionless groups as independent quotients between each pair of terms can immediately by obtained. To these dimensionless groups, the form factors derived from the equations defining the boundary conditions must be added [16,17]. According to the pi theorem, such zero-dimensional groups, and not the individual parameters of the problem of non-zero dimension in general, are the only ones that govern or determine the solution of the problem [18].…”