Mathematical modeling of heat and mass transfer in domainof solidifying alloy

In the paper the mathematical model, numerical algorithm and example of cylindrical casting solidification are presented. In particularthe casting made from Cu-Zn alloy is considered.It is assumed that the temperature correspondingto the beginning of solidification is time-dependent and it is a function of temporary alloy component concentration. The course of macrosegregation has been modeled using the mass balances inthe set of control volumes resulting from a domain discretization. The balances have been constructed in different ways, in particular under theassumption of instant equalization of alloy chemical constitution (a lever arm rule), next the Scheil model (e.g. Sczygiol 2000, Publ Czest UnivTechn Monographs, 71) has been used and finally the broken line model (Curran et al. 1980, Appl Math Modelling, 4, 398–400) has been taken into account. On a stage of numerical algorithm construction the boundary element method has been used in the variant called BEM using discretization in time (Curran et al. 1980, Appl Math Modelling, 4, 398–400; Sichert 1989, Technischen Fakultat der Universitat Erlangen; Szopa 1999, Publ. of the Silesian Univ. of Techn, 54) supplemented by the alternating phase truncationprocedure(Majchrzak and B.Mochnacki 1995, Engineering Analysis with Boundary Elements, 16, 99–121; Lar 2003, Application of generalized FDM in numerical modelling of moving boundary problems, Doctoral Theses, Czestochowa).