Global analysis of heat transfer considering three-dimensional unsteady melt flow in CZ crystal growth of oxide

The conventional global model of heat transfer for the Czochralski (CZ) crystal growth of oxides is based on a pseudo-steady axisymmetric assumption. However, because oxide melt flow is commonly three-dimensional and unsteady, an approach to formulate a global model in which a three-dimensional unsteady melt flow is taken into account was proposed in this study. This approach couples a conventional global model of heat transfer and a model of a three-dimensional, unsteady melt flow using two interface models. The newly developed global model was validated and used to investigate the effect of a three-dimensional, unsteady melt flow on oxide crystal growth. The results indicate that the effect of a three-dimensional, unsteady melt flow is too large to be neglected when the crystal rotational Reynolds number is relatively large. It was found that a three-dimensional, unsteady melt flow shifts the critical Reynolds number at which interface inversion occurs at a much lower value than that obtained using a conventional model based on a pseudo-steady axisymmetric assumption.