Solution of the direct alloy solidification problem including the phenomenon of material shrinkage

In the paper, we describe the solution technique for solving the direct problem of the alloy solidifying within the casting mould with the phenomenon of material shrinkage taken into account. Due to the difference between densities of the liquid and solid phases, the shrinkage of metal often appears during the solidification. The investigated process is modeled by means of the solidification in the temperature interval basing on the heat conduction equation with the source element enclosed which includes the latent heat of fusion and the volume contribution of solid phase. Whereas the shrinkage of metal is modeled by the proper application of the mass balance equation.