RADIATION HEAT-TRANSFER OF A CZOCHRALSKI CRYSTAL-GROWTH FURNACE WITH ARBITRARY SPECULAR AND DIFFUSE SURFACES

A numerical method is presented for predicting radiation heat transfer from axisymmetric bodies consisting of numerous arbitrary ring elements. Each ring element has the combined characteristics of specular and diffuse surfaces. The accuracy of the method was verified using a simple configuration. Good agreement between the present numerical and analytical solutions was obtained, and the effect of specular reflectivity was investigated. As a numerical example, radiation heat transfer of the Czochralski crystal growth apparatus was presented. The effect of specular reflection on temperature distribution on the various surfaces was examined. The present radiation transfer method was combined with the finite element package ABAQUS for conduction analysis, and the effect of specular reflectivity on temperature distribution and surface heat flux was investigated.