Two-dimensional solidification in a rectangular enclosure has been analyzed, taking into account the effects of natural convection and considering the convective and radiative boundary conditions at the surface of the mold and at the top of the enclosure. The bottom is taken as insulated. The dimensionless equations governing the unsteady velocity profiles in the melt and the unsteady temperature profiles in the melt, the solid, and the mold are solved by finite-difference methods, using the alternating direction implicit technique for the vorticity and the stream function. The effect of natural convection on the heat transfer at the interface and on the movement and shape of the interface is found to be significant compared to the results obtained by neglecting natural convection in the melt. © 1981 Taylor 8 Francis Group, LLC.