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 arb...

The simulation of chemically reacting ows in speci c situations is a basic instrument in natural sciences in order to understand complex phenomena (e.g., salt concentrations in oceans) as well as in engineering sciences (e.g., the optimization of the Czochralski growth in semiconductor industries, see e.g. [7, 15]). The objective of the paper is two-fold: First, we will present a rst-order time...

The axisymmetric flows with swirl or rotation were solved by a hybrid scheme with lattice Boltzmann method for the axial and radial velocities and finite-difference method for the azimuthal (or swirl) velocity and the temperature. An incompressible axisymmetric lattice Boltzmann D2Q9 model was proposed to solve the axial and radial velocities through inserting source terms into the two-dimensio...

In this paper we describe a semianalytical approach to computing the temperature and thermal stress inside a III-V compound grown with the Czochralski technique. An analysis of the growing conditions indicates that the crystal growth occurs on the conductive time scale. A perturbation method for the temperature field is developed for an arbitrary crystal profile using the Biot number as a (smal...