Radiative heat transfer in curved specular surfaces in Czochralski crystal growth furnace

A numerical investigation of radiative heat transfer constructed by curved surfaces with specular and diffuse reflection components is carried out. The ray tracing method is adopted for the calculation of view factors, in which a new my emission model is proposed. The second-degree radiation ring elements are introduced, which are of engineering importance and numerical efficiency. The accuracy of the method is analyzed and verified using a simple configuration. The present computation using the proposed ray emission model is in good agreement with the analytical 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 specular reflection and the meniscus. The combined effects of the specular reflection and the meniscus should be considered in precision heat transfer control of a CZ apparatus.