Boundary element model of microsegregation during volumetric solidification of binary alloy

In the paper the mathematical model of heat and mass transfer processes proceeding in the domain of casting is discussed. In particular, the volumetric solidification of a binary alloy under the assumption that the temperature is only time-dependent is analyzed. From the practical point of view such situation takes place when the casting is produced in typical moulding sand. The differential equation describing the course of solidification and cooling processes is presented in Sect. 1. In this equation the capacity of an internal heat source results from the Mehl-Johnson-Avrami-Kolmogorov theory [1, 2], at the same time the constant number of nuclei is accepted, while the rate of the solid phase growth is proportional to the second power of undercooling below the liquidus temperature. The macroscopic model is coupled with a microsegregation one (Sect. 2). This process is analyzed at the level of a single grain. The distribution of the alloy component in the control volume corresponding to the final grain radius is found on a basis of the boundary element method using discretization in time [3, 4]. The examples of numerical computations are also presented.