The effects of an axially imposed magnetic field on convection and solute segregation during Bridgman growth of a non-dilute multicomponent system Pb0.8Sn0.2 Te were studied using a finite-element model. The model considers heat and mass transport, fluid motion, solid/liquid-phase change and magnetic damping. The main objectives are to provide a quantitative understanding of the complex transport phenomena during solidification in a magnetic field, to provide estimates of the required magnetic field strength for low gravity growth, and to assess the role of magnetic damping for space and earth growth control. Numerical results for both vertical and horizontal growth configurations are presented. In addition to full-scale simulation, a revised scaling analysis is also presented.