Radiative heat transfer in silicon floating zone furnace with specular reflection on concave surfaces

A numerical study of radiative heat transfer in silicon floating zone crystal growth furnace with the needle-eye technique has been carried out. Both diffuse and specular reflections are considered on the concave surface of the silicon melt. The radiation element method is employed to solve the radiative heat transfer, in which the ray tracing method is adopted to calculate the view factors among curved diffuse and specular surfaces. The accuracy of the method is verified by good agreement with the analytical solution in a simple concave configuration system. The effects of view factors and the specular reflection of the surfaces of the melt, the crystal and the inductor on radiative heat transfer of a floating zone furnace are discussed. It is found that the specular reflection on the surfaces of melt and inductor tends to increase the heat flux or decrease the temperature gradient on the silicon melt surface. The view factors are changed remarkably with the variation of the concave surface shape, and consequently, affect strongly the radiative heat transfer.