Theoretical Investigation of Buoyancy-driven Cavity Flow by Using Finite Element

This research presents a mathematical model (finite element) to calculate the flow due to natural convection and heat transfer in enclosures. In this study, the equations was built according to suppose the flow two-dimensional and steady. Moreover, the equations are adopted from the finite element method and used in the stream function-vorticity form to allow for complex geometries and irregular boundaries. The two sides of walls (top and bottom) are perfectly insulated and completely conducting. The results from the current model are agreement with previous published results. The both temperature and flow fields in solid walls at theoretical results of isothermal contour lines were verified by comparing with the useful experimental results. The results of heat transfer are calculated through enclosures containing square and circular cavities. It was found that a large reduction up to 38% can be achieved in the heat transfer rates over walls by using walls including cavities, for the cases studied. For the same area ratio, the results indicated that the enclosures containing square were supplied better insulation when compared to the circular ones. Also increase the dependence of heat transfer on geometry with increase of Rayleigh number