Two dimensional, thermosolutal convection in molten Pb-Sn housed within a square enclosure, is simulated using a spectral method. The predictions illustrate two regimes of liquid convection which develop in response to simultaneous horizontal temperature and species concentration gradients applied to the system. Sherwood numbers for the high Schmidt number fluid are quite high, and change markedly depending upon the regime of operation. Heat transfer rates are only moderately affected by convection due to the low Prandtl number of the melt. The predictions at relatively large Rayleigh number and buoyancy ratio display highly oscillatory behavior in a manner consistent with previous experimental observations.