# Vortex shedding around a heated square cylinder under the influence of buoyancy

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## Abstract

The influence of buoyancy on vortex shedding and heat transfer from a cylinder of square cross-section exposed to a horizontal stream has been studied.Unsteady Navier-Stokes and energy equations are solved numerically using a control volume approach. Flow field has been analysed for a wide range of Reynolds number (which is based on the cross-sectional height of the cylinder) and Grashof number with Richardson number between 0 to 1. Our results show that the centerline symmetry of the wake is lost and the cylinder experiences a downwards lift when the buoyancy effect is considered. Vortex shedding suppression doesn’t occur in the present case in which the cylinder is exposed to a horizontal cross-flow. Heat transfer from the cylinder increases due to increase in Reynolds number and Grashof number.

## Keywords

Vortex Heat Transfer Reynolds Number Shear Layer Strouhal Number## List of symbols

*C*_{L}Lift coefficient

*C*_{p}Pressure coefficient

*c*_{p}Specific heat at constant pressure

- \(\overline {C_{\text {L}}} \)
Time-averaged lift coefficient

- \(\overline {C_{\text{D}}} \)
Time-averaged drag coefficient

- \(\overline {C_{\text {p}}} \)
Time-averaged pressure coefficient

*g*Gravitational acceleration

- Gr
Grashof number =

*g*β (*T*_{w - T_0})*H*^{3}/ν^{2}*H*Height of the cylinder

- Nu(
*t*) Local Nusselt number

- Nu
_{M}(*t*) Surface average heat transfer at each face of the cylinder

- Nu
_{total}(*t*) Total heat transfer from the cylinder

- \(\overline {{\text {Nu}}} \)
Time-average local Nusselt number on the surface of the cylinder

- \(\overline {{\text{Nu}}_{{\text {total}}}} \)
Total mean Nusselt number on the cylinder

*p*Dimensionless pressure

*Pr*Prandtl number =μ

*c*_{ p }/κ- Re
Reynolds number =

*UH*/ν- Ri
Raichardson number =

*Gr*/*Re*^{2}- St
Strouhal number =

*fH*/*U**T*Period of vortex shedding/dimensional temperature

*T*_{0}Dimensional lower temperature

*T*_{w}Dimensional higher temperature

*t*Dimensionless time

- \(\overline t \)
Dimensional time

*U*Reference horizontal velocity

*u**x*-component of velocity*y*Vertical distance

## Greek symbols

- β
Thermal coefficient of volume expansion

- ε
A small positive quentity

- θ
Dimensionless temperature

- ν
Kinematic viscosity coefficient

- κ
Thermal conductivity

- μ
Co-efficient of viscosity

- ρ
Fluid density

## Subscripts

- 0
In the undisturbed fluid

*w*At the wall

## Superscripts

- −
Dimensional quentity

## Notes

### Acknowledgments

One of the authors (S.B.) wish to thank CSIR, India for providing financial support.

## References

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