In Japan, high-level radioactive liquid waste (HLLW) produced in the reprocessing of spent nuclear fuels from nuclear power plants is to be vitrified and disposed in a deep geological repository. In the vitrification process, HLLW is mixed with high-temperature molten glass in a melter and discharged through a nozzle installed at the bottom of the melter. In this study, fluid flow with heat transfer of molten glass discharged from the nozzle was simulated numerically to predict the condition in the melter, where experimental visualization is hard to be carried out due to high temperature and corrosive environment. One-fluid formulation of three dimensional Navier-Stokes equations, a continuity equation, and an energy equation were solved by a standard finite volume method with VOF as an air-liquid interface tracking method. The viscosity of the molten glass was given as a function of its temperature and the concentration of insoluble platinum group metals (PGM) contained in HLLW. Simulation results indicated that the diameter of a molten glass jet increased with the temperature at the bottom of the melter and it decreased with the concentration of PGM. It suggests that the temperature and the concentration of PGM at the bottom of the melter are predictable by the measurement of the diameter of the molten glass jet.