Applications of generalized integral transform technique in the rapid solidification of metallic metals in the planar flow casting process / Aplicações da técnica de transformação integral generalizada na solidificação rápida de metais metálicos no processo de fundição em fluxo planar

Abstract

The Planar Flow Casting (PFC) is a single-stage fast solidification technique to produce thin metallic ribbons. The objective of this research is to develop a mathematical model to analyze the phenomenon of heat transfer and phase change during the formation of the puddle, to determine the interface position and velocity and the temperature profile. The applied methodology consists of the use of the energy balance, where the equations of the energy (liquid and solid phases), and the equation of the interface are transformed through the Generalized Integral Transform Technique (GITT) being solved by the NDSolve routine of the Matemathica. This tool was capable to solve problem, can study the fast cooling of metals and obtain ribbons of thickness controlled by the speed of the wheel and for the heat transfer coefficient. Considering that the height of the pool is very small and the process time is very short, many eigenvalues were used to obtain the solution convergence. The results of the temperature distribution along the length of the puddle, the evolution of the solidification front and the interface velocity were compared with existing results in the literature, obtaining good harmony.