The work carried out during the 4 year research activity can be barely classified in two main lines. On the one hand, a considerable effort is taken to address issues related with the verification of multi-dimensional and transient solutions that are obtained by numerical simulations. Within the studied cases, we can consider cases of piston-cylinder ows within geometries similar to those of hermetic reciprocating compressors.This issue is mentioned in Part I. On the other hand, numerical simulations of different phenomena have been performed. More emphasis has been given to the natural convection ow within enclosures. This is explained in Part II. The case extensively studied has been the natural convection ow. The natural convection ow within enclosures has attracted the attention of many researchers due to its potential to model numerous applications of engineering interest, such as cooling of electronic devices, air ow in buildings, heat transfer in solar collectors, among others. The natural convection studies corresponding to the parallelepipedic enclosures can be classified into two elementary classes: i) heating from a horizontal wall (heating from below); ii) heating from a vertical wall. The characteristic example of the former case is the Rayleigh-B_enard ow, however this research is on the cavities heated from the side. This configuration is referred commonly as the differentially heated cavity.