The influence of rotating magnetic fields (RMF) on species transport and interface stability during the growth of Cd0.96Zn0.04Te:In crystals by using the traveling heater method (THM), under microgravity and terrestrial conditions, is numerically investigated. The numerical results are compared to ground and space experiments. The modeling of THM under ground conditions shows very deleterious effects of the natural convection on the morphological stability of the growth interface. The vertical flow transports the liquid of low Te concentration from the dissolution interface to the growth interface, which is consequently destabilized. The suppression of this flow, in low-gravity conditions, results in higher morphological stability of the growth interface. Application of RMF induces a two flow cell pattern, which has a destabilizing effect on the growth interface. Simulations performed by varying the magnetic field induction in the range of 1-3 mT show optimal conditions for the growth with a stable interface at low strength of the magnetic field (B = 1 mT). Computations of indium distribution show a better homogeneity of crystals grown under purely diffusive conditions. Rotating magnetic fields of B = 1 mT induce low intensity convection, which generates concentration gradients near the growth interface. These numerical results are in agreement with experiments performed during the FOTON M4 space mission, showing good structural quality of Cd0.96Zn0.04Te crystals grown at very low gravity level. Applying low intensity rotating magnetic fields in ground experiments has no significant influence on the flow pattern and solute distribution. At high intensity of RIVIF (H = 50 mT), the buoyancy convection is damped near the growth front, resulting in a more stable advancing interface. However, convection is strengthening in the upper part of the liquid zone, where the How becomes unsteady. The multi cellular unsteady flow generates temperature oscillations, having deleterious effects on the growth process. (c) 2015 Elsevier B.V. All rights reserved.