A computational fluid dynamics model was developed to support the testing of a laboratory-scale waste glass melter. This work focuses on providing an understanding of how the heat flux convected from the melt pool is affected by the forced bubbling and by the foam layer underneath the cold cap formed by reaction gases. Simulations were performed for high-level waste glass simulants with viscosities near the minimum and maximum values that are expected during the Hanford tank waste vitrification campaign. The model resolves the forced convection bubbling in the molten glass and bubbles in the foam that forms beneath the cold cap. The glass with higher viscosity shows the formation of significantly larger bubbles to overcome the higher viscous force. The foaming thickness under the cold cap in higher viscosity cases is cleared less easily than the low viscosity glass case. However, the percentage of foam in contact with the cold cap is decreased at higher viscosity since the higher viscous force tends to prevent direct contact. This trend is reversed when there is no forced convection supplied by the bubblers. The heat fluxes at the bottom of the cold cap are compared for cases with and without forced convection bubbling. As expected, the convective heat flux increases with bubbling, and the average values for heat transfer coefficients from the CFD show reasonable agreement with Nusselt number correlations for flat plates.