RADIATIVE HEAT-TRANSFER IN CURVED SPECULAR SURFACES IN CZOCHRALSKI CRYSTAL-GROWTH FURNACE

A numerical investigation of radiative heat transfer constructed by cu rved surfaces with specular and diffuse reflection components is carri ed out. The ray tracing method is adopted for the calculation of view factors, in which a new my emission model is proposed. The second-degr ee radiation ring elements are introduced, which are of engineering im portance and numerical efficiency. The accuracy of the method is analy zed and verified using a simple configuration. The present computation using the proposed ray emission model is in good agreement with the a nalytical solution. As a numerical example and engineering application , the effects of the specular reflection and the meniscus of the melt surface in Czochralski (CZ) crystal growth are investigated. A marked temperature decrease in the melt surface is found by introducing specu lar reflection and the meniscus. The combined effects of the specular reflection and the meniscus should be considered in precision heat tra nsfer control of a CZ apparatus.