Solidification of an alloy by cooling the vertical sides of a rectangular mold is considered. By estimates of the order of magnitudes of terms in the governing equations, a parameter range map is derived. This contains 14 entries, each of which signifies a particular set of qualitative properties of the solidification process. In each case, quantitative estimates for solidification time, degree of undercooling and segregation, are given. The qualitative and quantitative estimates are confirmed and illustrated by time-dependent numerical simulation of a few typical solidification histories.