Numerical investigation using SIMPLE algorithm with QUICK scheme for natural convection and heat transfer in the enclosure bounded by a solid wall and with heat transfer and radiation coupled in natural convection has been conducted. The various parameters are: Rayleigh number (from 10 3 to 10 5 ), dimensionless conductivity of bounding wall (from 0 to 100), dimensionless wall thickness (from 0 to 0.6) and radiation emissivity of all surfaces (from 0 to 1). The results suggest that flow and heat transfer are influenced by radiation. Radiation is a dominant action on flow and heat transfer. With increase of the thermal conductivity of wall, flow and heat transfer turn stronger. The temperature distribution changes obviously. When the thermal conductivity of wall is over a certain critical number, the increasing trend of flow and heat transfer may disappear. With increase of enclosure wall thickness, flow and heat transfer turn slighter. When the enclosure wall thickness is over a certain critical number, the flow and heat transfer will turn slow. conduction, natural convection, radiation, couple, numerical simulation Citation:Zhan N Y, Yang M, Xu P W. A two-dimensional study on natural convection and heat transfer in the enclosure with heat transfer and radiation coupled in natural convection. Sci China Tech Sci, 2010, 53: 991−999,

Natural convection of air is numerically simulated in a 3-dimensional rectangular cavity heated from below using SIMPLE algorithm with a QUICK scheme. The results suggest that when all lateral walls are adiabatic, the fluid rolls occur along the long axis. When the Rayleigh number is smaller, the flow is of 2-dimensional character, and the rolls shapes are similar. The average Nusselt numbers in the central part of the cavity are similar. The average Nusselt numbers in the part near by the cavity are different. According to the comparison of 3-dimensional results with 2-dimensional results, the flow patterns and heat transfer in the central part of the cavity can be assumed as a 2-dimensional flow, While those in the part near by the cavity can not. With increasing Rayleigh number, the flow is 3-dimensional characteristic. The 3-dimensional result accords with the experimental result. When all lateral walls are adiabatic, the ten rolls occur along the long axis. But when lateral walls are heated or cooled, the rolls disappear along the long axis and two rolls occur along the short axis. The rotation direction of the rolls is reversed. When Rayleigh number is over some critical value, flow and heat transfer will be asymmetry, indicating unsteady oscillation occurs. By nonlinear analyses, it is shown that with increasing Rayleigh number, flow and heat transfer will change from steady state to unsteady state through HOPF bifurcation, and transition to chaos will occur through multi-periodical oscillation. Critical Raleigh number, 3-dimensional character, lateral boundaries, nonlinear characteristic, bifurcation Citation:Zhan N Y, Xu P W, Sun S M, et al. Study on the stability and 3-dimensional character for natural convection in a rectangular cavity heated from below.