The realistic boundary condition of the surface temperature varying with time is used in the heat transfer analysis of the solidification of a binary eutectic alloy system. The system occupies a semi-infinite region and consists of a solid zone, a freezing zone, and a liquid zone. The heat released in the freezing zone is treated as a discontinuous heat generation. The solid-fraction distribution in the freezing zone, given as a function of temperature, is solved simultaneously with the temperature distribution, which is given as a function of distance within the freezing zone. Using the “heat balance integral” technique, the method for the solution of the temperature distribution and the thickness of each region is given. As an example, the results are shown in graphical form for an Al-5 percent Cu alloy.