Two- and three-dimensional simulations of flow and heat transfer around rectangular cylinders

This numerical study investigates the forced convection heat transfer from and flow topology around isothermal rectangular cylinders. The effects of various cross-sectional aspect ratios (AR = 0.25–4), Reynolds numbers (Re = 30–200), and Prandtl numbers (Pr = 0.7, 5) are examined on the results. Two or three-dimensional simulations are conducted depending on the Re and AR employed. The results show that the near primary vortices (Kármán wake) undergo a downstream transition to the two-layered vortices, followed by a transition from the two-layered vortices to the secondary vortices for AR ≤ 1. For smaller aspect ratios, the prevailing of the secondary vortices is further accelerated, i.e., they emerge at a lower Re and a shorter downstream distance from the cylinder. Three types of secondary vortices distinguished based on their shape, strength, and generation mechanism were observed. A geometric criterion (spacing ratio) for the onset of evolution of the two-layer structure is proposed for each AR. It is observed that the sensitiveness of the Nusselt number to AR and Re can be ascribed to the change in the scenarios of the flow separation and reattachment (flow regimes), vortex strength, and wake-recirculation size (Lr). The Nusselt number grows with increasing Re and Pr but diminishes with AR. The relationship between the average Nusselt number and Lr is direct in the steady flow, while they are inversely linked in the two- and three-dimensional unsteady flow. Reducing AR from 4 to 0.25, depending on Re and Pr, leads to a 90%–170% enhancement in the Nusselt number, whereas increasing AR amplifies the total heat transfer due to an enlargement in the heat transfer surfaces. The second law of thermodynamics analysis reveals that cylinders with smaller AR generate lower entropy (destroy lower exergy); therefore, they are more efficient.