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Experimental and numerical study of turbulent flow and heat transfer inside hexagonal duct

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Abstract

Flow and heat transfer characteristics in transition and turbulent regions are studied experimentally and numerically in a horizontal smooth regular hexagonal duct under constant wall temperature boundary condition covering a range of Reynolds number from 2.3 × 103 to 52 × 103. Two types of k-omega (standard and shear stress transport (SST)) and three types of k-ε (standard, renormalization (RNG), and realizable) turbulence model are employed for transition and turbulent regions, respectively. Both average and fully developed Darcy friction factor and Nusselt number are presented as a function of Reynolds number. It is seen that k-omega SST and k-ε realizable turbulence models gave the best agreement with the experimental data in transition and turbulent regions, respectively. All the experimental results are correlated within an accuracy of ±13 % and ±7 % for Nusselt number and Darcy friction factor, respectively. Results obtained in this study are compared with circular duct results using hydraulic diameter.

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Abbreviations

A c :

Cross sectional area of the hexagonal duct (m2)

A s :

Heat transfer surface area of the hexagonal duct (m2)

c p :

Specific heat (kJ kg−1 K−1)

C 1, C 2 :

Constant coefficients in Eqs. (8), (9)

C μ :

Constant

D h :

Hydraulic diameter of the hexagonal duct (m)

\( \dot{E} \) :

Total electric power input (W)

F :

Average Darcy friction factor

f fd :

Fully developed Darcy friction factor

f x :

Peripherally averaged local Darcy friction factor

F :

View factor

h m :

Average heat transfer coefficient (W m−2 K−1)

k :

Turbulent kinetic energy (m2 s−2)

k c :

Thermal conductivity (W m−1 K−1)

l :

Turbulence length scale (m)

L :

Axial length of the hexagonal duct (m)

\( \dot{m} \) :

Mass flow rate of the airflow through the hexagonal duct (kg s−1)

n 1, n 2 :

Power indices in Eqs. (8), (9)

Nu fd :

Fully developed Nusselt number

Nu m :

Average Nusselt number

Nu x :

Peripherally averaged Nusselt number

P :

Wetted perimeter of the hexagonal duct (m)

Pr :

Prandtl number

Δp :

Axial pressure drop across the hexagonal duct (Pa)

q w,x′′:

Peripherally averaged wall heat flux at x-position (W m−2)

\( \dot{Q}_{c} \) :

Steady-state forced convection heat transfer from the hexagonal duct to the airflow (W)

\( \dot{Q}_{l} \) :

Conduction heat loss from the hexagonal duct assembly to the surroundings (W)

\( \dot{Q}_{r} \) :

Radiation heat loss from ends of the hexagonal duct to the surroundings (W)

Re :

Reynolds number

T :

Temperature (K)

T b :

Bulk mean temperature (K)

T bi, T bo :

Mean temperatures of the airflow at the inlet and outlet (K)

T i :

Inlet temperature (K)

T w :

Wall temperature of the hexagonal duct (K)

T ∞ :

Ambient temperature (K)

u i :

Velocity component in the i direction (m s−1)

u j :

Velocity component in the j direction (m s−1)

\( \left( { - \overline{{u_{\text{j}}^{\prime } T^{\prime } }} } \right) \) :

Turbulent heat flux (m s−1 K)

\( \left( { - \overline{{u_{\text{i}}^{\prime } u_{\text{j}}^{\prime } }} } \right) \) :

Turbulent shear stress (m2 s−2)

u, v, w :

Velocity components (m s−1)

U :

Mean air velocity in the hexagonal duct (m s−1)

U(x):

Mean velocity at x-position (m s−1)

x, y, z :

Cartesian coordinates (m)

x i :

Coordinate in the i direction (m)

x j :

Coordinate in the j direction (m)

y p :

Distance of the centroid of the nearest cell from the wall (m)

y + :

Dimensionless distance from wall

Θ :

Dimensionless temperature

ε :

Turbulent dissipation rate (m2 s−3)

ε e :

Surface emissivity

τ w :

Wall shear stress (Pa)

τ w,x :

Peripherally averaged wall shear stress at x-position (Pa)

ρ :

Fluid density (kg m−3)

σ :

Stefan-Boltzmann constant (W m−2 K−4)

υ :

Kinematic viscosity of the airflow (m2 s−1)

ω :

Specific dissipation rate (s−1)

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Acknowledgments

This work is funded by the Unit of Scientific Research Projects of Gazi University under the project BAP 06/2008-38: Experimental and numerical investigation of heat transfer for hydrodynamically and thermally developing flow in a hexagonal duct under constant wall temperature.

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Authors and Affiliations

  1. Faculty of Engineering, Department of Mechanical Engineering, Gazi University, 06570, Maltepe-Ankara, Turkey

    Oğuz Turgut & Mehmet Sarı

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  1. Oğuz Turgut
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  2. Mehmet Sarı
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Correspondence to Oğuz Turgut.

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Turgut, O., Sarı, M. Experimental and numerical study of turbulent flow and heat transfer inside hexagonal duct. Heat Mass Transfer 49, 543–554 (2013). https://doi.org/10.1007/s00231-012-1101-z

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