Prandtl number effects on steady state natural convection flow and heat transfer in a square cavity

Steady-state natural convection induced by the temperature difference between the two vertical walls of a square cavity (aspect ratio L = 1.0) has been investigated. The governing equations have been solved by a numerical method which employs conservative upwind finite-difference approximations. To study the effects of Prandtl number (Pr), numerical solutions have been obtained in a wide range of this parameter (0.001 to 1000) for different Rayleigh numbers (Ra). The streamline and isotherm plots at Ra = 100,000 have been presented, and the salient flow features have been discussed. On the basis of flow and heat-transfer results for Pr of at least 1.0, three different flow regimes have been identified. The Nusselt number (Nu) correlations have been obtained in these regimes. The Rayleigh-number limits at which the secondary cells appear in the core region have also been investigated for different Prandtl numbers.