Heat Transport

Abstract

In a later chapter we progress to asking questions about the stability of the growth process and to this end we need to understand the heat transfer processes throughout the crystal pulling assembly. We have seen that numerical simulation provides physical insight into the nature of the flows in the melt and their coupling to the thermal boundary conditions but that to deal with questions of stability one must properly take account of the crystal-melt interface as a thermodynamic phase boundary whose shape represents the solution of the problem and not a boundary condition. Such problems are known as Stefan problems (see for example Ockendon and Tayler [79]). First, though, we determine the temperature field in the cooling crystal.