The radiation heat exchange in monoellipsoidal mirror furnaces is considered. In particular, the radiative interaction between the sample and the mirror is studied. This interaction is formulated analytically taking into account multiple reflections at the mirror. It is shown that the effect of these multiple reflections in the heating process is quite important, especially up to the third reflection, and, as a consequence, the effect of the mirror reflectance in the temperature field is quite strong. A conduction-radiation model is thus formulated to study the temperature field in slender, cylindrical samples (at this stage convection effects in the melt are not considered). This model is used to simulate the heating process in the floating-zone technique in microgravity conditions; important parameters like the Marangoni number (that drives the thermocapillary flow in the melt), and the temperature gradient at the melt-crystal interface are estimated. The model is validated comparing with experimental data, the agreement is very good both qualitative and quantitatively. (C) 2002 Elsevier Science B.V. All rights reserved.