The binary alloy problem in an expanding domain: the microsegregation problem

A general numerical model of microsegregation and solidification in coarsening (i.e. expanding) secondary dendrite arms is developed. General governing equations representing the diffusive heat and mass transfer in an expanding domain are presented. The governing equations are transformed using enthalpy type variables (to deal with the moving solidification interface s(t)) and a Landau transformation (to deal with the expanding domain X(t)). This transformation allows for a fixed grid 'node jumping' numerical solution. The resulting solutions compare favorably with existing experiments and require only a fraction of the CPU time of alternative approaches.