The amount of fission products remaining in the molten mass of material that could result from core melt-through must be known to evaluate the heat loads on various parts of the structure, and depends on many factors too numerous to mention here. The present work was confined to an approximate evaluation of diffusion and internal convection as mass transfer mechanisms under fairly quiescent conditions. This condition was chosen because it would result in larger amounts of heat-generating fission products remaining in the melt than would be the case with more violent agitation. Internal heat generation in a molten slab of fluid cooled primarily from the upper surface would create a temperature gradient which, at some critical value, would cause internal convection currents due to the greater buoyancy of the hotter material in the lower portions of the melt. These convection currents enhance both the heat and mass transfer from the interior of the molten material to the surface. The heat transfer and rate of release of fission products (using yttrium oxide as an example) from a slab of molten fuel and steel were calculated and the results compared with a diffusion calculation. A sensitivity analysis was performed and the effects of wide variations in the thickness of the melt, viscosity, coefficient of thermal expansion, diffusion coefficient, specific heat, and thermal conductivity are reported. For the base case of yttrium oxide in 200 tons of molten UO2 and steel in a slab 17.1 cm thick, the time required to release 80% of the fission product was 9 h, compared with 40 days for the case where a diffusion model was assumed. Although these results are very approximate, being based on estimated thermophysical properties and idealized assumptions, they show that the effect of internal convection on mass transfer is so important that it cannot be ignored in any process where its occurrence may be suspected.