It is well known that A segregation similar to that found in steel castings is the result of an
upward flow of inter-dendritic liquid. The liquid steel rises because the density of the liquid in
contact with the solid decreases with temperature decrease. The inter-dendritic liquid steel is
thus lighter than the bulk liquid steel. Channels or A segregates are formed because the rising
liquid steel must move towards the hotter center of the casting. As the temperature increases,
the inter-dendritic liquid can dissolve the solid and a channel is formed. Once formed, a channel
continues to grow, producing the well-developed A segregate in the final casting. Thus, detailed
information during solidification in the presence of natural convection is of importance.
Because of the non-linearity and complexity of the problem, analytic solutions of the solidification
of pure metals and alloys are limited. In order to understand the interaction of fluid flow
in solidifying system, a two-dimensional finite-element program which can be applied for
solving the solidification of pure metals and alloys, including the effects of natural convection in
liquid, was developed using a temperature-recovery scheme. Two numerical examples demonstrate
the accuracy and the capability of the program developed.