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

Abstract

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 3 to 10 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.