On the nature and structure of possible three-dimensional steady flows in closed and open parallelepipedic and cubical containers under different heating conditions and driving forces

Possible natural transport mechanisms in cubical and shallow cavities with different heating conditions (from below or from the side) are investigatedby means of numerical solution of the non-linear model equations and multiprocessor computations. Attention is focused on a variety of three-dimensional steady effects that can arise in such configurations in the case of low-Pr liquids (silicon melt) even for relatively small values of the temperature gradient due to localized boundary effects and/or true instabilities of the flow. Such aspects are still poorly known or completely ignored owing to the fact that most of the existing experiments focused on the subsequent onset of oscillatory flow, or on the case of transparent (Pr >> 1) liquids. The influence of bothbuoyancy and surface tension forces is considered. The role played by the geometrical constraints and degrees of freedom in determining the three-dimensional structure of the flow field is discussed. Some effort is devotedto elucidate the results within the framework of existing (state-of-the-art) theories and to illustrate the deviation of results pertaining to a real three-dimensional geometry with respect to earlier two-dimensional models.