A direct numerical simulation of heat mass transfer processes in the melt under the influence of surface tension forces on free surfaces during germanium crystal growth by the floating zone (FZ) method under microgravity conditions is performed. Development in time, and interaction between thermal and solutal kinds of Marangoni convection in the molten zone taking into account the temperature dependence of melt viscosity are analyzed. The obtained results explain anomalous distributions of Ga dopant in Ge single crystals grown aboard Russian Photon series spacecrafts (SC).