A finite element method of solution for laminar convection flows was used to obtain the flow, temperature, and heat transfer distributions for a heated copper block immersed in a tank of water simulating the debris tray cooling problem that can result after a core meltdown in a liquid-metal-cooled fast breeder reactor. Careful iteration has allowed the solution to be taken up to the onset of turbulence value of Gr · Pr ≃ 5 × 107. Comparison of the numerical solution with experimental results shows very good agreement. Local and average Nusselt numbers for this confined-flow situation are then derived from the solution, and it is shown that the existing correlations for flat plates in an infinite medium can be used to predict to a first approximation the behavior in the more complex geometries simulating the debris tray.