ABSTRACT
The influence of opposing-buoyancy mixed convection from a square cylinder in a vertical channel has been studied at Reynolds numbers (Re) = 1–100, Richardson numbers (Ri) = 0 to −1, and blockage ratios (β) = 10–50% for air as a working fluid. The onset of a steady to a time-periodic regime is found for Ri = 0 (at Re = 35, 65, 74, and 62), Ri = −0.5 (at Re = 12, 39, 48, and 54), and Ri = −1 (at Re = 9, 30, 39, and 50) for β = 10%, 25%, 30%, and 50%, respectively. The initiation of flow separation is also determined. Finally, the correlations of Strouhal number, drag coefficient, and the Colburn heat transfer factor were obtained.
Nomenclature
CD | = | total drag coefficient |
CDF | = | friction drag coefficient |
CDp | = | pressure drag coefficient |
CL | = | lift coefficient |
Cp | = | constant-pressure specific heat of the fluid (J/kgK) |
d | = | side of a square cylinder (m) |
f | = | frequency of vortex shedding (1/s) |
FD | = | drag force per unit object length (N/m) |
FDF | = | frictional force per unit object length (N/m) |
FDP | = | pressure force per unit object length (N/m) |
FL | = | lift force per unit object length (N/m) |
g | = | acceleration due to gravity (m/s2) |
Gr | = | Grashof number |
h | = | local convective heat transfer coefficient (W/m2K) |
= | average convective heat transfer coefficient (W/m2K) | |
H | = | computational domain height (m) |
jh | = | Colburn heat transfer factor |
k | = | thermal conductivity of the fluid (W/mK) |
Nu | = | local Nusselt number |
= | average Nusselt number | |
ns | = | normal direction |
p | = | pressure |
Pr | = | Prandtl number |
Re | = | Reynolds number |
Ri | = | Richardson number |
St | = | Strouhal number |
t | = | time |
T | = | temperature (K) |
TP | = | time period of one cycle |
T∞ | = | fluid temperature at the inlet (K) |
Tw | = | surface temperature of the square cylinder (K) |
u | = | x-velocity component |
v | = | y-velocity component |
V∞ | = | average velocity of fluid at the inlet (m/s) |
x | = | stream-wise coordinate |
Xd | = | downstream distance (m) |
Xu | = | upstream distance (m) |
y | = | crossways coordinate |
βv | = | volume expansion coefficient (1/K) |
β | = | blockage ratio |
θ | = | temperature gradient |
μ | = | fluid viscosity (Pa s) |
ρ | = | fluid density (kg/m3) |
Superscript | = | |
∗ | = | dimensional value |
Nomenclature
CD | = | total drag coefficient |
CDF | = | friction drag coefficient |
CDp | = | pressure drag coefficient |
CL | = | lift coefficient |
Cp | = | constant-pressure specific heat of the fluid (J/kgK) |
d | = | side of a square cylinder (m) |
f | = | frequency of vortex shedding (1/s) |
FD | = | drag force per unit object length (N/m) |
FDF | = | frictional force per unit object length (N/m) |
FDP | = | pressure force per unit object length (N/m) |
FL | = | lift force per unit object length (N/m) |
g | = | acceleration due to gravity (m/s2) |
Gr | = | Grashof number |
h | = | local convective heat transfer coefficient (W/m2K) |
= | average convective heat transfer coefficient (W/m2K) | |
H | = | computational domain height (m) |
jh | = | Colburn heat transfer factor |
k | = | thermal conductivity of the fluid (W/mK) |
Nu | = | local Nusselt number |
= | average Nusselt number | |
ns | = | normal direction |
p | = | pressure |
Pr | = | Prandtl number |
Re | = | Reynolds number |
Ri | = | Richardson number |
St | = | Strouhal number |
t | = | time |
T | = | temperature (K) |
TP | = | time period of one cycle |
T∞ | = | fluid temperature at the inlet (K) |
Tw | = | surface temperature of the square cylinder (K) |
u | = | x-velocity component |
v | = | y-velocity component |
V∞ | = | average velocity of fluid at the inlet (m/s) |
x | = | stream-wise coordinate |
Xd | = | downstream distance (m) |
Xu | = | upstream distance (m) |
y | = | crossways coordinate |
βv | = | volume expansion coefficient (1/K) |
β | = | blockage ratio |
θ | = | temperature gradient |
μ | = | fluid viscosity (Pa s) |
ρ | = | fluid density (kg/m3) |
Superscript | = | |
∗ | = | dimensional value |
Acknowledgements
The authors would like to thank two anonymous reviewers for their positive comments on this work.