The problem of numerical modeling of directional solidification of TiAl refractory intermetallics aboard the MAXUS 8 sounding rocket is considered. The research is of relevance to the FP6 Integrated project IMPRESS (Intermetallic Materials Processing in Relation to Earth and Space Solidification). Attention is paid to columnar-to-equiaxed microstructure transition (CET) phenomenon and mushy zone evolution in Ti-45.9Al-8Nb (at %) alloy being processed in TEM 01-3M high-temperature (up to 17000C) furnace. In this three-zone resistive furnace the “bent” temperature profile is applied with two strongly different axial thermal gradients, presumably allowing the achieving of CET conditions along the sample of 160 mm length. Temperature profile evolution is defined by power-down furnace operation. 2D-numerical study of heat transfer and realtime-scale solidification dynamics of TiAl-Nb under zero gravity approximation is performed. The approaches used for solution of Navier-Stokes equations and phase transition (Stefan) problem are briefly described. The solidification time is shown to be satisfying the 12-minute microgravity limit aboard a MAXUS. The position and the time at which CET may be triggered are predicted and confirmed in line with the Hunt diagram. The comparison is performed of model predictions with the real microstructure of TiAl-Nb reference sample solidified on-ground in TEM 01-3M facility.