Three-dimensional simulations of natural convection in a sidewall-heated cube

Abstract

A high-resolution, finite difference numerical study is reported on three-dimensional natural convection of air in a differentially heated cubical enclosure over an extensive range of Rayleigh number from 10 to 10. The maximum number of grid points is 122 × 62 × 62. Solutions to the primitive variable formulation of the incompressible Navier-Stokes and energy equations are acquired by a control-volume-based procedure together with a higher-order upwind-differencing technique. The field characteristics at large-time limits are examined in detail by state-of-the-art numerical visualizations of the three-dimensional results. The emergence of the well-defined boundary layers and the interior core at high Rayleigh numbers is captured by elaborate numerical visualizations. Both the similarities and discrepancies between the three- and two-dimensional computations are pointed out. These emphasize the need for three-dimensional calculations to accurately determine the flow characteristics and heat transfer properties in realistic, high-Rayleigh-number situations.