Calculating Radiative Heat Transfer in anAxisymmetric Closed

Radiative heat transfer plays an important part in the Czochralski crystal growth process , but it is diicult to simulate numerically because of the amount of computational time required. This paper describes the parallelization of a code simulating radiative heat transfer in the crystal and in the region above the melt containing gas under the assumption of axial symmetry. This code allows arbitrary grid reenements of the various material interfaces. The code can be used to study the eeect of radiative heat transfer near the melt-crystal-gas interface. The results demonstrate how the accuracy of the ux at the interfaces depends on the grid resolution, and parallelization is required to obtain the higher grid resolutions. This paper presents numerous steps which have been taken to validate the code. Timing and the parallel eeciency studies indicate that this code makes eecient use of the computational resources.