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An experimental and three-dimensional numerical study on the convective heat transfer inside a trapezoidal duct under constant wall temperature

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Abstract

In this study, steady-state forced convection heat transfer and pressure drop characteristics for hydrodynamically fully developed thermally developing three-dimensional turbulent flow in a horizontal smooth trapezoidal duct with corner angle of 75° and hydraulic diameter of 0.043 m were both experimentally and numerically investigated in the Reynolds number range from 2.6 × 103 to 67 × 103 for isothermal conditions. Results have shown that there is a good agreement between the present experimental and numerical results.

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Abbreviations

A :

inner surface area (i.e. in contact with the air) of the trapezoidal cross-sectioned duct (m2)

A c :

cross-sectional area of the trapezoidal duct (m2)

C 1, C 2, C 3 :

constant coefficients in Eqs. (7), (8), and (10) (–)

D h :

hydraulic diameter of the passageway through the considered trapezoidal duct (m)

\( \mathop E\limits^{ \cdot } \) :

steady-state electric power supplied to heat the test section (W)

f :

average Darcy friction factor (–)

F :

view factor for thermal radiation from the duct ends to its surroundings (–)

\( \overline{h} \) :

average heat transfer coefficient for the trapezoidal cross-sectioned duct’s inner surface and the forced air flow passing through the duct (W m−2 K−1)

H :

height of the trapezoidal cross-section duct (m)

k :

thermal conductivity of air (W m−1 K−1)

L :

axial length of the test section (m)

n 1, n 2, n 3 :

power indices in Eqs. (7), (8), and (10) (–)

Nu :

local Nusselt number (–)

\( \overline{Nu} \) :

average Nusselt number for the steady state heat transfer between the test section’s inner surface and the air flow using D h (–)

P :

wetted perimeter (m)

ΔP :

pressure drop along the test section (Pa)

Pr :

Prandtl number for the air flowing through the duct (–)

\( \mathop {Q_{c} }\limits^{ \cdot } \) :

steady-state rate of convective heat transfer from the test section’s inner surface to the air flowing through the duct (W)

\( \mathop {Q_{l} }\limits^{ \cdot } \) :

steady-state rate of heat loss by conduction from the test section to the ambient environment (W)

\( \mathop {Q_{r} }\limits^{ \cdot } \) :

steady-state rate of thermal radiation from both ends of the test section to the surroundings (W)

Re :

hydraulic diameter-based Reynolds number of the air flow (–)

T b :

mean bulk temperature of the air flow in the duct (K)

T bi, T bo :

mean bulk temperature of the air flow at the inlet and exit of the test section, respectively (K)

T w :

surface temperature of the test section (K)

T ∞ :

ambient temperature (K)

T i :

inlet temperature (K)

U :

mean velocity of the air flow in the trapezoidal duct (m s−1)

\( {{\Updelta}}T_{\text{lm}} \) :

logarithmic mean temperature difference (K)

x, y, z :

cartesian coordinates (–)

Θ:

dimensionless temperature profile (–)

ε :

emissivity (–)

υ :

kinematic viscosity of air (m2 s−1)

ρ :

density of the air (kg m−3)

σ :

Stefan–Boltzmann constant (W m−2 K−4)

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Acknowledgments

The authors wish to thank the State Planning Organization for financial support of this project.

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Authors and Affiliations

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

    Nevzat Onur, Oğuz Turgut, Kamil Arslan & Özen Kurtul

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  1. Nevzat Onur
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  2. Oğuz Turgut
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  3. Kamil Arslan
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  4. Özen Kurtul
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Correspondence to Nevzat Onur.

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Onur, N., Turgut, O., Arslan, K. et al. An experimental and three-dimensional numerical study on the convective heat transfer inside a trapezoidal duct under constant wall temperature. Heat Mass Transfer 45, 263–274 (2009). https://doi.org/10.1007/s00231-008-0423-3

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  • DOI: https://doi.org/10.1007/s00231-008-0423-3

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