The heat transfer and fluid flow in a glass melter has been analyzed by a finite element code developed for this study. For two different thermal boundary conditions at the glass surface, the Navie-Stokes equations of the stream function-vorticity type and the energy equation are solved on the rectangular elements. After validating the code by comparing the flow field for the prescribed free stream temperature condition, with earlier results, the computation has been carried out for various mass flux conditions. The streamline pattern and temperature field for each case exhibit the characteristics of the glass flow rate and then enable one to determine whether the specific condition is desirable.