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ABSTRACT
The effects of cross-buoyancy mixed convection from a square cylinder in the proximity of a plane wall are studied for Reynolds number (Re) = 1–100, Richardson number (Ri) = 0–2, and gap ratio (G) = 0.25–1 at Prandtl number (Pr) = 0.7. The flow observed is steady for G = 0.25 and 0.5. The transition from a steady to a time-periodic system is observed for G = 1, and it is found at Re = 56, 60, and 74 for Ri = 0, 1, and 2, respectively. With increasing G and/or Ri, the drag coefficient and average Nusselt number increase for all Re values studied and the lift coefficient decreases with increasing Ri except at Re = 1. Maximum heat transfer augmentation is found about 89% at G = 0.5 (Re = 20, Pr = 0.7, Ri = 0) with respect to the corresponding value at G = 0.25 (Re = 20, Pr = 0.7, Ri = 0). Lastly, the correlations of drag coefficient and heat transfer have been obtained.
Notations
| CD | = | Total drag coefficient |
| CDf | = | Friction drag coefficient |
| CDp | = | Pressure drag coefficient |
| CL | = | Total lift coefficient |
| CP | = | Pressure coefficient |
| cp | = | Specific heat of the fluid (J/kg.K) |
| CV | = | Control volume |
| D | = | Side of a square obstacle (m) |
| FD | = | Drag force per unit side of the square obstacle (N/m) |
| FL | = | Lift force per unit side of the square obstacle (N/m) |
| f | = | Frequency of vortex shedding (1/s) |
| g | = | Acceleration due to gravity (m/s2) |
| G | = | Gap ratio |
| Gr | = | Grashof number |
| H | = | Height of computational domain (m) |
| h | = | Local convective heat transfer coefficient (W/m2.K) |
| = | Average convective heat transfer coefficient (W/m2.K) | |
| jh | = | Colburn heat transfer factor |
| k | = | Thermal conductivity of the fluid (W/m.K) |
| Ld | = | Downstream distance (m) |
| Lu | = | Upstream distance (m) |
| m | = | Velocity gradient |
| N | = | Control volumes around one side of square obstacle |
| Nu | = | Local Nusselt number |
| = | Average Nusselt number | |
| p | = | Pressure |
| pS | = | Local pressure at a point on the surface of an obstacle (N/m) |
| p∞ | = | Reference pressure (N/m) |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| Ri | = | Richardson number |
| St | = | Strouhal number |
| t | = | Time |
| T | = | Temperature (K) |
| TP | = | Time period for one cycle |
| T∞ | = | Fluid temperature at the inlet (K) |
| Tw | = | Surface temperature of the square obstacle (K) |
| U∞ | = | Average fluid velocity at the inlet (m/s) |
| u*, v* | = | Components of velocity in x- and y-directions, respectively (m/s) |
| x*, y* | = | Streamwise and transverse coordinates, respectively (m) |
| Greek symbols | = | |
| βv | = | Coefficient of volumetric expansion (1/K) |
| ρ | = | Fluid density (kg/m3) |
| μ | = | Dynamic viscosity of the fluid (Pa.s) |
| δ | = | Smallest cell size (m) |
| θ | = | Dimensionless temperature |
| Superscript | = | |
| * | = | Dimensional value |
Notations
| CD | = | Total drag coefficient |
| CDf | = | Friction drag coefficient |
| CDp | = | Pressure drag coefficient |
| CL | = | Total lift coefficient |
| CP | = | Pressure coefficient |
| cp | = | Specific heat of the fluid (J/kg.K) |
| CV | = | Control volume |
| D | = | Side of a square obstacle (m) |
| FD | = | Drag force per unit side of the square obstacle (N/m) |
| FL | = | Lift force per unit side of the square obstacle (N/m) |
| f | = | Frequency of vortex shedding (1/s) |
| g | = | Acceleration due to gravity (m/s2) |
| G | = | Gap ratio |
| Gr | = | Grashof number |
| H | = | Height of computational domain (m) |
| h | = | Local convective heat transfer coefficient (W/m2.K) |
| = | Average convective heat transfer coefficient (W/m2.K) | |
| jh | = | Colburn heat transfer factor |
| k | = | Thermal conductivity of the fluid (W/m.K) |
| Ld | = | Downstream distance (m) |
| Lu | = | Upstream distance (m) |
| m | = | Velocity gradient |
| N | = | Control volumes around one side of square obstacle |
| Nu | = | Local Nusselt number |
| = | Average Nusselt number | |
| p | = | Pressure |
| pS | = | Local pressure at a point on the surface of an obstacle (N/m) |
| p∞ | = | Reference pressure (N/m) |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| Ri | = | Richardson number |
| St | = | Strouhal number |
| t | = | Time |
| T | = | Temperature (K) |
| TP | = | Time period for one cycle |
| T∞ | = | Fluid temperature at the inlet (K) |
| Tw | = | Surface temperature of the square obstacle (K) |
| U∞ | = | Average fluid velocity at the inlet (m/s) |
| u*, v* | = | Components of velocity in x- and y-directions, respectively (m/s) |
| x*, y* | = | Streamwise and transverse coordinates, respectively (m) |
| Greek symbols | = | |
| βv | = | Coefficient of volumetric expansion (1/K) |
| ρ | = | Fluid density (kg/m3) |
| μ | = | Dynamic viscosity of the fluid (Pa.s) |
| δ | = | Smallest cell size (m) |
| θ | = | Dimensionless temperature |
| Superscript | = | |
| * | = | Dimensional value |
Acknowledgments
The authors would like to thank two anonymous reviewers for their positive comments on this work.