A numerical simulation study, using finite element method, was carried out to examine the temperature and concentration fields in the dissolution process of silicon into germanium melt. This work utilized a simplified configuration which may be considered to be similar material configuration to that used in the Vertical Bridgman growth methods. The concentration profile for the Si-Ge sample processed using this technique shows increasing transport silicon into the melt with time, moreover, a flat stable interface is observed. The mass and momentum equations for fluid flow, the energy and the solute mass transport were numerically solved. Results showed good agreements with experiments.