# Flow and heat transfer analysis around tandem cylinders: critical gap ratio and thermal cross-buoyancy

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## Abstract

The focus of the current numerical investigation is to study the fluid flow and mixed convective (thermal cross-buoyancy) heat transfer of incompressible fluid across identical cylinders organized in a confined tandem configuration because of their enormous engineering and industrial applications such as heat exchange tubes, electronic cooling, twin chimney stacks, cooling tower, etc. The involved flow and energy equations are solved for different gap ratios (*S*/*D* = 2.5, 3, 3.5, 4, 5, and 5.5) with varying Richardson number (*Ri* = 0, 0.5, and 1) at Reynolds number *Re* = 100, Prandtl number *Pr* = 0.7 and wall confinement *β* = 25% by using a finite volume method-based commercial solver ANSYS Fluent. It is found that after a certain gap ratio there is a drastic change in the physical parameters and after that gap ratio the change is gradual; this gap ratio is termed as a critical gap ratio. The introduction of thermal cross-buoyancy (*Ri* > 0) plays a deep impact on the physical parameters, and it is to be noted that the critical spacing shifts towards a lower value with increasing *Ri*. The analysis of lift coefficients shows that the fluctuations in lift signal shift from zero average value at *Ri* = 0 towards the nonzero negative average value for the tandem cylinders at *Ri* > 0. The local Nusselt number shows the shift in the front stagnation point on both cylinders with increasing thermal cross-buoyancy. The drag coefficient and Nusselt number of the downstream cylinder are always less than the upstream cylinder, but the percentage increment in the physical parameters of the downstream cylinder after critical spacing is much more than its upstream counterpart.

## Keywords

Confined cylinders Tandem configuration Cross-buoyancy mixed convection Gap ratio Strouhal number and power spectrum density## List of symbols

*C*_{D}Drag coefficient

*C*_{L}Lift coefficient

*C*_{P}Fluid specific heat (J/kg K)

*D*Cylinder diameter (m)

*f*Vortex shedding frequency (Hz)

*g*Acceleration due to gravity (m/s

^{2})*Gr*Grashof number \( \left( {\frac{{g\beta_{v} \left( {T_{w} - T_{\infty } } \right)D^{3} }}{{\eta^{2} }}} \right) \)

*h*_{Φ}Local coefficient of heat transfer (W/m

^{2}K)*H*Vertical length of channel (m)

*k*Thermal conductivity of fluid (W/mK)

*L*Horizontal length of channel (m)

*n*Direction normal to cylinder surface

*Nu*_{Φ}Local Nusselt number

*P*Dimensionless pressure \( \left( {\frac{{\bar{p}}}{{\rho U_{\text{avg}}^{2} }}} \right) \)

*Pr*Prandtl number \( \left( {\frac{{\mu C_{P} }}{k}} \right) \)

*Re*Reynolds number \( \left( {\frac{{U_{\text{avg}} D}}{\eta }} \right) \)

*Ri*Richardson number \( \left( {\frac{Gr}{{Re^{2} }}} \right) \)

*S*Spacing between cylinders (m)

*St*Strouhal number \( \left( {\frac{fD}{{U_{\text{avg}} }}} \right) \)

*t*Dimensionless time \( \left( {\frac{{U_{\text{avg}} \mathop t\limits^{\_} }}{D}} \right) \)

*T*Temperature (K)

*T*_{w}Temperature of cylinders (K)

*T*_{∞}Temperature of inlet stream (K)

*U*_{avg}Average inlet velocity of fluid (m/s)

*U*_{x}Dimensionless velocity in

*x*-direction \( \left( {\frac{{\bar{u}_{x} }}{{U_{\text{avg}} }}} \right) \)*U*_{y}Dimensionless velocity in

*y*-direction \( \left( {\frac{{\bar{u}_{y} }}{{U_{\text{avg}} }}} \right) \)*X*Dimensionless distance in

*x*-direction \( \left( {\frac{x}{D}} \right) \)*X*_{D}Downstream distance of channel (m)

*X*_{U}Upstream distance of channel (m)

*Y*Dimensionless distance in

*y*-direction \( \left( {\frac{y}{D}} \right) \)

## Greek symbols

*β*Blockage ratio (

*D*/*H*)*β*_{v}Volumetric expansion coefficient (K

^{−1})*δ*Smallest grid size (m)

*η*Kinematic viscosity of fluid (m

^{2}/s)*θ*Dimensional temperature

*μ*Viscosity of fluid (Ns/m

^{2})*ρ*Density of fluid (kg/m

^{3})*Φ*Polar angle (°)

## Superscript

- −
Dimensional quantity

## Subscripts

- w
Surface of cylinders

*∞*Inlet stream

- 1
Upstream cylinder

- 2
Downstream cylinder

## Notes

### Compliance with ethical standards

### Conflict of interest

The author declares that there is no conflict of interest statement.

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