Analysis of experiments involving a cylindrical column of lead in the process of freezing downward or alternatively, of melting upward from the base of the container, showed that heat transfer rates associated with Be´nard convection are less under transient conditions than at steady-state. Analysis of experiments involving the freezing of lead-tin alloys (0.2 – 1.6 wt. percent Sn) showed that the same heat transfer correlation for Be´nard convection could be applied, provided the upper bounding “interface” was located on the solidus isotherm for planar and cellular alloy growth, and on the liquidus, for cellular-dendritic alloy growth.