In this paper a two-dimensional glass tank model is presented for an electrically heated compact glass melting unit operated at the University of Bayreuth. The model is solved using the ANSYS commercial finite elemental analysis (FEM) software package. The glass tank model considers coupled thermo-electrical fluid flow effects and describes the heat transfer, electrical field and fluid flow patterns. The effect of radiation has also been included by considering the temperature dependent effective radiative thermal conductivity in the fluid analysis. The model has been validated with measured temperature data from the existing glass melting unit and achieves good agreement between calculated and measured temperatures in different operation modes.