# Analysis of laminar flow across a triangular periodic array of heated cylinders

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## Abstract

The laminar flow and heat transfer across a triangular periodic array of heated cylinders are simulated computationally and analyzed. The study has been carried out at Reynolds number 10–100 for fluid volume fraction ranging from 0.7 to 0.99 and Prandtl number ranging from 0.7 to 50. The size of the wake region increases continuously with an increase in the Reynolds number for all values of fluid volume fraction. The recirculation bubble from the rear of a cylinder is reaching the front of the next cylinder in the same column of the periodic array for low values of free volume fraction, but this is not the case with the highest free volume fraction, i.e., 0.99. At high Reynolds number, the flow is separating early on the cylinder surfaces. The wake size at higher Reynolds number 75 and 100 for the lowest free volume fraction 0.7 is more in comparison with the wake size at free volume fraction 0.99, which is explained by plotting the location of flow separation against Reynolds number for both the extreme values of free volume fractions, i.e., 0.7 and 0.99. The isovorticity contours are concentrated in the vicinity of the cylinders on increasing the Reynolds number irrespective of free volume fraction and then convected downstream. On increasing free volume fraction, the friction and pressure drags in the array decrease. The increase in Reynolds number also results in the decrease in the values of the individual (friction and pressure drag coefficients) as well as total drag coefficients for all values of free volume fraction. At high values of Reynolds number, the emergence of carbuncle or thermal spike on isotherm near the cylinder’s surface is observed where the value of the local Nusselt number is observed low. The heat transfer improves and the Nusselt number increases as the Reynolds number and/or Prandtl number increases. On the contrary, heat transfer decreases as free volume fraction increases.

## Keywords

Triangular array Cylinders Drag coefficient Free volume fraction Periodicity Flow separation Isotherms Nusselt number## List of symbols

*C*_{D}Overall mean drag coefficient

*C*_{DF}Friction/viscous drag coefficient

*C*_{DP}Pressure drag coefficient

*C*_{DR}Ratio of pressure and friction drag coefficients

*C*_{P}Coefficient of pressure

*c*_{p}Specific heat of the fluid (J kg

^{−1}K^{−1})*D*Cylinder diameter (m)

*F*Dimensionless drag force (

*F*_{D}/*µU*)*F*_{D}Drag force (N m

^{−1})*F*_{DF}Friction drag force (N m

^{−1})*F*_{DP}Pressure drag force (N m

^{−1})*G*Grid size

*h*Convective heat transfer coefficient (W m

^{−2}K^{−1})*k*Thermal conductivity of fluid (W m

^{−1}K^{−1})*L*Center to center distance between cylinders (m)

*Nu*Average Nusselt number

*p*Pressure

*p*_{f}Dimensionless free stream pressure

*p*_{θ}Dimensionless pressure on the surface of a cylinder

*Pr*Prandtl number

*r*Radius of the cylinder (m)

*Re*Reynolds number

*T*Dimensionless temperature

*T*_{d}Dimensional temperature (K)

*T*_{w}Temperature at the cylinders surface (K)

*T*_{∞}Free stream temperature (K)

*U*Volume-averaged fluid velocity (m s

^{−1})- u
Cross-stream velocity (m s

^{−1})*u*Dimensionless cross-stream velocity

- v
Stream-wise velocity (m s

^{−1})*v*Dimensionless stream-wise velocity

- x, y
Dimensional Cartesian coordinates (m)

*x, y*Dimensionless Cartesian coordinates

## Greek symbols

*α*_{sep}Angle of separation (°)

*ϕ*_{f}Porosity/free volume fraction

*µ*Viscosity of fluid (Pa s)

*ρ*Density of fluid (kg m

^{−3})*ψ*Stream function

*θ*Surface angle (°)

*ω*_{z}Dimensionless vorticity

## Notes

### Acknowledgements

The authors would like to thank the reviewers for their valuable suggestions and helpful comments, which have enriched the present work for the wider readership.

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