Numerical modeling becomes an important technique to study hydrothermal crystal growth since experimental measurements in hydrothermal autoclaves are extremely difficult due to the high pressure and high temperature growth conditions. In all existing models for hydrothermal growth, isothermal boundary conditions are assumed, although electric heaters are employed around the outside surface of the thick autoclave wall in practice. In this paper, a conjugate heat transfer model based on an industry size autoclave is developed to investigate the validity of such an assumption. The model includes not only turbulent fluid flow and heat transfer of the solution but also the heat conduction in the thick wall. The outside surfaces of the wall are under constant heat flux conditions, simulating electric resistance heating used in practice. Non-uniformity of the heat flux in the circumferential direction is also introduced in the model. The results indicate that the temperature at the solution/wall interface is far away from uniform. The isothermal wall boundary condition in previous efforts is questionable. Predictions of the isothermal wall model are analyzed. Parametric studies with the conjugate model show that total heat supply rate does not affect vertical uniformity dramatically. Heat loss can be lowered without affecting the flow and temperature fields if heaters are put half diameter or further away from the middle height (baffle) plane.
A conjugate heat transfer model for unconstrained melting of macroencapsulated phase change materials subjected to external convection
