Effect of thermal boundary condition of an inner cube on three-dimensional natural convection in a cubical

Abstract

We numerically investigated three-dimensional (3-D) natural convection in a vertical cubic enclosure with an inner cube for Rayleigh numbers (Ra) in the range of 103 ≤ Ra ≤ 106. For the inner cube at the center, four different thermal boundary conditions (adiabatic, neutral, and hot and cold isothermal conditions) were considered in order to investigate their effect on flow and thermal fields. For Ra = 103 and Ra = 104, single circulation appears regardless of the thermal boundary condition of the inner cube. When Ra = 105 and Ra = 106, the combined effects of the inner cube as a bluff body and the thermal condition imposed on the inner cube on the fluid flow and thermal fields are significant, and intensify the 3-D effect. Generally, for Ra = 105 and Ra = 106, the convective flow is characterized by the formation of two inner vortices embedded in the primary circulation, and by secondary vortices due to flow separation at the edge of the inner body. As Ra increases, the local Nusselt number varies rapidly in the vertical direction, which is supported by the temperature isosurfaces that form an S-shape. The total surface-averaged Nusselt numbers for the different cases have approximately the same profile with respect to the Rayleigh number as the power function.