TEMPERATURE-FIELD IN A CYLINDRICAL CRYSTAL HEATED IN A MONO-ELLIPSOID MIRROR FURNACE

The temperature field in a cylindrical solid crystal heated in a mono-ellipsoid mirror furnace is studied. The radiation intensity on the surface of the sample is obtained explicitly as a function of the parameters that define the problem. The resulting axisymmetric two-dimensional conduction-radiation model is solved numerically. The dependence of the maximum temperature in the crystal on several design parameters is analyzed. The importance of the radiation losses from the sample is assessed. When the slenderness of the crystal is large. the temperature field is practically unidimensional. A one-dimensional model to describe the heat transfer process is formulated; the agreement with the two-dimensional model is excellent. The simplified one-dimensional model is proposed for the analysis of the more difficult problem where the redistribution by the mirror of the radiation losses from the sample is considered.