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 (Nu3D) at low Ra as compared to the 2D situation. For increasing Ra, Nu3D approaches the 2D correlation, however, for the largest Ra, Nu3D is slightly larger than Nu2D and there is a local minimum in Nu3D/Nu2D 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.

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