Effect of Prandtl number and free-stream orientation on global parameters for flow past a heated square cylinder

Abstract

In this study, an in-depth examination of the aerodynamic parameters involving forced and mixed convection around a heated square cylinder is presented. The ranges of Prandtl number (Pr), Richardson number (Ri), and flow orientation (α) are kept as 0.71 ≤ Pr ≤ 1000, 0 ≤ Ri ≤ 1.6, 0° ≤ α ≤ 90°, while the Reynolds number (Re) and the cylinder orientation (ϕ) are kept fixed as Re = 100 and ϕ = 0°, respectively. The flow is considered as two-dimensional (2D), steady, laminar, incompressible, and viscous. The buoyancy effects are taken into account through the Boussinesq approximation. At lower Pr, the flow shifts from unsteady to steady with increasing Ri. This transition persists at higher Ri with increasing Prandtl values. The flow remains consistently unsteady at α = 90°. Isotherm crowding intensifies with higher Pr and/or Ri across all flow inclinations. Across the complete spectrum of flow angles, it is noted that the mean lift coefficient rises as the Richardson number increases. Additionally, the mean drag coefficient reaches its peak at Ri = 1.6 when Pr = 0.71. The findings reveal that the Strouhal number (St) rises as the Richardson number (Ri) increases, and it decreases as the Prandtl number (Pr) increases. The mean Nusselt number (Nu¯) demonstrates an upward trend as the Prandtl number increases, with Ri held constant. It is also observed that Nu¯ is more sensitive to the Prandtl number than the Richardson number and is maximum at Pr = 1000 for the selected range of flow orientations.