The effect of furnace configuration and ampoule design on the temperature field, the convection in the melt, the shape of the melt-solid interface, and the segregation of solute in the crystal are analyzed for the directional solidification of several dilute and non-dilute binary semiconductor alloys. The analysis is based on numerical calculations using a Petrov-Galerkin/finite-element method for solving the free-boundary problem that describes axisymmetric convection in the melt, the interface shape, and heat transfer in melt, crystal, and ampoule in a quasi-steady state model of the vertically stabilized Bridgman-Stockbarger system and for a furnace with a uniform temperature gradient imposed over a long section of ampoule. The flow in molten germanium grown in the Bridgman-Stockbarger system has two vertically-stacked toroidal cells. The top cell moves melt upward along the ampoule wall and is driven by the radial temperature gradients caused by the junction of the adiabatic and hot zones of the furnace. The cell adjacent to the melt/solid interface convects melt upward along the axis of the ampoule and exists because of the mismatch between the thermal conductivities of melt, crystal and ampoule. The relative intensities of the two cells depend on the values of the three conductivities and the magnitude of the axial temperature gradient. The upper cell is not present in the furnace with a uniform axial gradient; however, radial temperature gradients near the melt/crystal interface still drive convection. Adding a solute that is less dense than the bulk melt and that is preferentially incorporated upon solidification, such as silicon in germanium, decreases the intensity of the flow near the interface by increasing the melt density there. Radial temperature gradients interact with the solute field to cause the sideways diffusive instability predicted by Hart [J. Fluid Mech. 49 (1971) 279]. Calculation of the melt/crystal interface shape, radial segregation, and effective segregation coefficient for the growth of dilute gallium is germanium agree reasonably well with measurements of Wang [PhD Thesis (1984)] when an accurate description of heat transfer in the ampoule and furnace is included in the analysis.