A two-phase Mixture model is proposed to simulate the liquid-solid phase transition
of a Fe-0.82wt%C steel alloy under the effect of Marangoni flow. This model simplifies
computations by solving a single momentum and enthalpy equation for the mixture phase using
a three-dimensional finite volume method. The simulation involves solidifying a rectangular
ingot (100 × 10 × 100 mm3) from the cold bottom surface towards the hot-free surface at the top.
To facilitate heat exchange with the surrounding environment, a high heat transfer coefficient of
h = 600 W/m2/K was applied on the bottom surface to establish an upward solidification
direction. However, a lower heat transfer coefficient of 20 W/m2/K was applied on the top free
surface, which was considered flat. This study aims to examine the effect of Marangoni flow
generated by surface tension on flow and segregation patterns. The results show that the
Marangoni flow emerges at the free surface and penetrates into the liquid depth, leading to the
formation of hexagonal patterns along the liquid thickness. Upon full solidification, macro-
segregation also exhibits hexagonal structures, mirroring the stationary hexagonal shapes
generated by Marangoni flow.