Buoyancy Driven Flow Between Vertical Parallel Plates of Finite Width

In the present investigation, three-dimensional (3D) simulations have been carried out in order to study the influence of Rayleigh number (Ra^″, 0.1 to 1000) and the geometric proportions H/S (5 and 10) and W/S (2.5 to 20), where H is the duct height, S is the plate spacing, and W is the plate width. The Prandtl number is 0.72, and the thermal boundary condition is uniform heat flux. The results are compared to the corresponding two-dimensional (2D) situation that is approached when W/S is very large. The investigation is restricted to laminar flow. For H/S = 5, the 3D effects increase the Nusslet number (Nu_3D) at low Ra^″ as compared to the 2D situation. For increasing Ra^″, Nu_3D approaches the 2D correlation, however, for the largest Ra^″, Nu_3D is slightly larger than Nu_2D and there is a local minimum in Nu_3D/Nu_2D in the range 1 < Ra^″ < 100. The minimum occurs at smaller Ra^″ for increasing W/S. In general, it seems as the buoyancy driven flow between parallel plates of finite width can be characterized by four regimes: conduction regime, pressure regime, boundary layer regime, and turbulent regime.