In crystal growth autoclaves, dissolution zone and cristallisation zone are connected through a diaphragm. The flow regimes in such a configuration are quite complex, as they result from two buoyancy mechanisms, solutal and thermal, acting in opposite directions. In addition, the autoclave walls are thick and heat transfer in it strongly affect heat transfer in the bulk (conjugate problem).Several model with increasing difficulties have been numerically tested to calculate the bulk flow. For a thermal boundary condition with a flux imposed at the external wall, the temperature distribution along the internal wall is found to be almost linear.For ''thermosiphon'' configuration, the axisymmetric solution is completely different, but still the flow goes up along the internal wall inside the two zones. For three-dimensional solutions, the flow is going up along the axis in the crystallisation zone; showing that the axisymmetric solution is not realistic.In addition, the stability theory indicates that after a certain threshold, the solution would become anti-symmetric and thus will be three-dimensional too.

A numerical procedure for solving the combined free and forced laminar convection in the entrance region of an axisymmetric geometry is presented. The governing equations associated with the three-dimensional developing flow are formulated in terms of velocity-vorticity-temperature and transformed into a finite difference form. The transformed equations are solved in a false transient way using a numerical scheme based on the alternating-direction implicit method. Results presented for the case of an horizontal annulus reveal the effect of natural convection on the developing axial flow and temperature field.

Ce travail a pour objet l'étude de l'écoulement laminaire de convection forcée en régimes dynamique et thermique non établis dans la région d'entrée d'un espace annulaire compris entre deux cylindres coaxiaux et isothermes. La résolution du problème a été faite par la méthode des différences finies. Ainsi nous avons obtenu les champs de vitesse et de température pour plusieurs combinaisons du rapport des rayons, du nombre de Reynolds, du nombre de Peclet et de la température du fluide à l'entrée. Ce qui nous a permis d'établir des corrélations pour les longueurs d'établissement dynamique et thermique et d'analyser le transfert de chaleur au niveau des parois.