Analysis of Flow Structures and Global Parameters across a Heated Square Cylinder in Forced and Mixed Convection

In the present study, numerical simulations are performed to identify the role of Reynolds number (Re), Richardson number (Ri) and free-stream orientations (α) on flow structures, aerodynamic parameters and heat transfer characteristics for the conditions (20 ≤ Re ≤ 120, 0° ≤ α ≤ 90° and 0 ≤ Ri ≤ 1.6). Prandtl number (Pr) and cylinder orientation (ϕ) are kept fixed at 0.71 and 0°. The Oberbeck–Boussinesq approximation is used to account for buoyancy effects. The governing equations of continuity, momentum and energy are discretized on a colocated body-fitted grid by employing a finite difference method. A viscous implicit pressure correction scheme is employed to advance the discrete solution in time. Contour maps of mean/steady drag coefficient and Nusselt number on (α-Ri) plane are plotted for 20 ≤ Re ≤ 120. From these contour maps, it is possible to identify the ranges of parameters (α, Ri) that can yield a relatively high mean/steady heat transfer rate accompanied by relatively low values of mean/steady drag coefficient. For [70° ≤ α ≤ 90°, 0 ≤ Ri ≤ 1.6], such a scenario is possible for any Re ∈ [20, 120]. The Strouhal number is observed to be maximum for Re = 120 at α = 45° and Ri = 1.2. Mean or steady coefficient of lift for any free-stream orientation (α ≠ 0°) is found to be highest at Re = 20 and Ri = 1.6. Sensitivity of (CD)Ri = 0.0 to α is observed to be minimum for Re = 20 and maximum for Re = 120. Sensitivity of the ratio CD(Ri,α)/CD(0,α) to Re is observed to be lower for unsteady flows than for steady flows, and it decreases with an increase in Re at a fixed value of Ri. Mean Nusselt number (Nu) in the forced flow regime increases significantly with an increase in Re at a fixed α. The Nusselt number is observed to be more sensitive to Ri for steady flows than for unsteady flows. The percentage increase in the ratio Nu(Ri,α)/Nu(0,α) for the entire range of Re is found to be 14.07%, 14.13%, 11.74% and 10.62% at α = 30°, 45°, 60° and 90°. At a fixed Ri, the Nusselt number ratio is found to decrease with an increase in Re for the entire range of α except for α = 90°. It is observed that the rate of heat transfer from the faces of the cylinder increases with an increase in Re for the entire ranges of α and Ri.