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

The solidification and cooling processes taking place in the casting domain can be described by the system of partial differential equations and adequ ate boundary, geometrical, physical and initial conditions, From the mathem atical point of view, the so-called moving boundary problem should be consi dered and the task can be effectively solved using numerical methods. In th is paper, the alloy's solidification is considered. In differential equatio ns 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 mode l, because the temperatures limiting the mushy zone subdomain are a functio n of the alloy component's concentration (a binary alloy is taken into acco unt). Two macrosegregation models are constructed on the basis of the lever -arm law and Scheil's equation, respectively. In terms of numerical computa tion, the boundary element method (heat transfer model) and the control vol ume method (macrosegregation) are applied. The typical numerical solutions presented in the literature do not take into account the relationships betw een 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.