This paper presents a model for the unsteady species transport for the growth of alloyed semiconductor crystals during the vertical Bridgman-Stockbarger process with a steady axial magnetic field. During growth of alloyed semiconductors such as germanium-silicon (GeSi) and mercury-cadmium-telluride (HgCdTe), the solute’s concentration is not small, so that density differences in the melt are very large. These compositional variations drive compositionally driven buoyant convection, or solutal convection, in addition to thermally driven buoyant convection. These buoyant convections drive convective transport, which produces nonuniformities in the concentration in both the melt and the crystal. This transient model predicts the distribution of species in the entire crystal grown in a steady axial magnetic field. The present study presents results of concentration in the crystal and in the melt at several different stages during crystal growth.