Steady three‐dimensional thermal convection in a vertical rectangular enclosure

Abstract

AbstractThe numerical study of the steady 3D thermal flow regimes in a vertical enclosure with side‐wall heating and cooling is considered; a primitive variable Galerkin finite element method is used for the simulation in the Boussinesq approximation. The model consists of a rectangular box with vertical and horizontal aspect ratios, respectively, of lz = 12 (vertical length to box width) and ly = 8 (horizontal length to box width). The two large vertical plates are maintained at different and constant temperatures, and the remaining walls are assumed to be perfectly conducting. The enclosure is filled with a fluid of Prandtl number Pr=0.71, and the Grashof number Gr, based on the spacing between the large vertical walls, is up to 1.2 × 104. The 3D results presented herein were obtained with a 11 × 9 × 53 node mesh in half of the enclosure by imposing symmetry at the mid‐plane. The solution in the mid‐plane is compared with a 41 × 121 2D solution and laboratory observations at various Gr values. The transition between the monocellular and multicellular natural convective regimes is determined. The 3D aspect of the flow is illustrated and compared with the 2D solution. Near the onset of multicellular flow predicted by linear stability theory, the 2D and 3D simulations exhibit a steady multicellular structure. The calculated flow patterns are compared to visualizations obtained by smoke traces in physical experiments.