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ABSTRACT
Numerical computations were brought up to study the effect of opposing buoyancy mixed convection (Ri = 0 to − 1) flow of power law shear-thinning fluids past a confined cooled square bluff body at Prandtl numbers (Pr) = 1, 50 and Reynolds numbers (Re) = 1–40. Irrespective of the n, Ri, Pr, and Re, the flow separation is delayed with increasing confinement (β). The vortex shedding and flow separation start earlier for shear-thinning fluids than Newtonian fluid. For opposing buoyancy (Ri < 0), the vortex shedding starts earlier on increasing Pr (except for n = 0.2, Ri = −1). Also, the periodic unsteady transition appears at some higher value of Re on increasing Ri for fixed Pr. The drag coefficient (CD) value reduces with the decrease in n, whereas the maximum CD is noted for Newtonian fluids. The maximum augmentation in the heat transfer was reached about 9 and 36% on comparing with Newtonian fluids and forced convection case, respectively, and also the corresponding maximum compression in heat transfer was found about 15 and 5%, respectively. The numerical results have also been correlated for CD and the Colburn jh factor values for various Re, Pr, Ri, and n. In surplus, the effects of wall confinement ranging from β = 25 to 50% on flow separation and engineering output parameters were studied in a steady regime.
Nomenclature
| CD | = | total drag coefficient |
| cp | = | constant pressure specific heat of the fluid (J/kg.K) |
| CV | = | control volume |
| d | = | a side of the square obstacle (m) |
| FD | = | drag force (N/m) |
| g | = | gravitational acceleration (m/s2) |
| Gr | = | Grashof number |
| h | = | average convective heat transfer coefficient (W/m2.K) |
| H | = | horizontal length (m) |
| I2 | = | second invariant of rate of strain tensor |
| jh | = | the Colburn heat transfer factor |
| k | = | thermal conductivity (W/m.K) |
| L | = | vertical height (m) |
| Ld | = | downstream distance (m) |
| Lu | = | upstream distance (m) |
| m | = | flow consistency index (Pa.sn) |
| n | = | power law index |
| Nu | = | average Nusselt number |
| p | = | pressure |
| Pe | = | Peclet number (RePr) |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| Ri | = | Richardson number |
| t | = | time |
| T | = | temperature (K) |
| Tw | = | square wall temperature (K) |
| = | inlet fluid temperature (K) | |
| = | 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 crosswise coordinates, respectively (m) |
| Greek symbols | = | |
| β | = | wall confinement |
| = | thermal expansion coefficient (K−1) | |
| Δ | = | smallest cell size (m) |
| ε | = | rate of deformation tensor |
| θ | = | temperature difference |
| η | = | power law viscosity of the fluid |
| ρ | = | fluid density (kg/m3) |
| τ | = | extra stress tensor |
| Superscript | = | |
| * | = | dimensional value |
Nomenclature
| CD | = | total drag coefficient |
| cp | = | constant pressure specific heat of the fluid (J/kg.K) |
| CV | = | control volume |
| d | = | a side of the square obstacle (m) |
| FD | = | drag force (N/m) |
| g | = | gravitational acceleration (m/s2) |
| Gr | = | Grashof number |
| h | = | average convective heat transfer coefficient (W/m2.K) |
| H | = | horizontal length (m) |
| I2 | = | second invariant of rate of strain tensor |
| jh | = | the Colburn heat transfer factor |
| k | = | thermal conductivity (W/m.K) |
| L | = | vertical height (m) |
| Ld | = | downstream distance (m) |
| Lu | = | upstream distance (m) |
| m | = | flow consistency index (Pa.sn) |
| n | = | power law index |
| Nu | = | average Nusselt number |
| p | = | pressure |
| Pe | = | Peclet number (RePr) |
| Pr | = | Prandtl number |
| Re | = | Reynolds number |
| Ri | = | Richardson number |
| t | = | time |
| T | = | temperature (K) |
| Tw | = | square wall temperature (K) |
| = | inlet fluid temperature (K) | |
| = | 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 crosswise coordinates, respectively (m) |
| Greek symbols | = | |
| β | = | wall confinement |
| = | thermal expansion coefficient (K−1) | |
| Δ | = | smallest cell size (m) |
| ε | = | rate of deformation tensor |
| θ | = | temperature difference |
| η | = | power law viscosity of the fluid |
| ρ | = | fluid density (kg/m3) |
| τ | = | extra stress tensor |
| Superscript | = | |
| * | = | dimensional value |
Acknowledgments
The authors would like to thank the Editor and the anonymous reviewers for their positive comments on this work.