We present a fully coupled model for the traveling heater method (THM) under microgravity conditions and a rotating magnetic field (RMF) and apply it to analyze the growth of cadmium zinc telluride (CZT). The model provides a self-consistent representation of fluid flow and heat and mass transfer in a liquid zone shaped by dissolution and growth interfaces that are computed to satisfy local transport and thermodynamic equilibrium conditions. The temperature, stream function, tellurium, and zinc profiles in the liquid are analyzed with and without the rotating magnetic field. Results show that the system is very sensitive to the growth rate under microgravity alone, leading to tellurium accumulation, a concave growth interface, and constitutional supercooling at faster growth rates. While RMF-induced convection mixes the zone, creates a more uniform composition, and makes the microgravity system less sensitive to growth rate variations, RMF can also lead to undesirable outcomes. In particular, for stronger RMF fields, flows are driven inward along the growth interface, and the resulting accumulation of tellurium near the centerline results in localized interface concavity and liquid supercooling. The mechanisms behind the above phenomena are clarified, and some advice is provided for applying the RMF appropriately to THM CZT growth under microgravity conditions. (C) 2016 Elsevier B.V. All rights reserved.