METHOD OF BOUNDARY VORTICITY FORMULATION AND ITS EFFECT ON HEAT TRANSFER IN ENCLOSURES
A mathematical model is developed to simulate a two-dimensional laminar free convection generated in a square cavity due to differential heating of the opposite walls. The system of governing differential equations is numerically solved using finite-differencing techniques. The boundary vorticity is calculated by different formulations -some are simple and others elaborate. The Nusselt numbers are determined at various Rayleigh numbers using the wall vorticity evaluated by different schemes. It is found that different vorticity-calculation methods produce different Nusselt numbers under the same exact physical conditions. The difference in the results thus obtained varied very widely at low as well as high Rayleigh number flow regimes. Some boundary vorticity formulations produce even numerical instabilities. The present results are compared with the existing numerical and experimental results which differ among themselves. Finally, it is concluded that the method of boundary vorticity has a dominant influence on the final outcome of the results, and that the sophisticated formulations are not necessarily better when low resolution grids are used in the wall boundary layers.