Boundary element model of coupled heat and mass transfer in solidifying castings

Abstract

The solidification and cooling processes taking place in the casting domain can be described by the system of partial differential equations and adequate boundary, geometrical, physical and initial conditions. From the mathematical point of view, the so-called moving boundary problem should be considered and the task can be effectively solved using numerical methods. In this paper, the alloy's solidification is considered. In differential equations describing the solidification process, the parameter called a substitute thermal capacity is introduced; in other words, the one domain approach is applied. The heat transfer model is coupled with the macrosegregation model, because the temperatures limiting the mushy zone sub-domain are a function of the alloy component's concentration (a binary alloy is taken into account). Two macrosegregation models are constructed on the basis of the lever-arm law and Scheil's equation, respectively. In terms of numerical computation, the boundary element method (heat transfer model) and the control volume method (macrosegregation) are applied. The typical numerical solutions presented in the literature do not take into account the relationships between heat transfer and macrosegregation processes or the models proposed are very complex and not effective. The solution presented in this paper seems to be sufficiently exact and very simple for numerical realisation.