Steady, Two-Dimensional, Natural Convection in Rectangular Enclosures With Differently Heated Walls

Numerical results are presented for steady natural convection in two-dimensional rectangular enclosures in which the side walls, top wall, and bottom wall are at uniform temperatures θ_s, θ_t, and θ_b, respectively, and θ_s > θ_t > θ_b. Raylight numbers ranging from 10⁴ to 10⁷ and aspect ratios of 1 and 1.5 were investigated. The top wall was modeled as an impermeable rigid surface or an impermeable free-moving boundary. The calculations reveal two flow regions. In the upper part of the enclosure two large counterrotating cells appear, separated by a descending plume of fluid. Near the bottom wall the flow is almost motionless and stably stratified. The temperature in the central portion of the enclosure is almost uniform due to mixing by the recirculating cells. A temperature inversion occurs near the top wall and is particularly noticeable at high Rayleigh numbers. At high Rayleigh numbers the flow breaks up into smaller cells. The result is that each main recirculation region develops a secondary counterrotating eddy within it. The condition of a free surface as the top wall boundary condition significantly affects the circulation and heat transfer throughout the flow domain. Numerical experiments reveal the extent to which the flow field in the enclosure is affected by an asymmetric specification of side-wall temperature boundary conditions.