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Numerical estimation of heat transfer characteristics for two-row plate-finned tube heat exchangers with experimental data

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Abstract

This study applies a three-dimensional computational fluid dynamics commercial software in conjunction with various flow models to estimate the heat transfer and fluid flow characteristics of the two-row plate-finned tube heat exchanger in staggered arrangement. The effect of air speed and fin spacing on the results obtained is investigated. Temperature and velocity distributions of air between the two fins and heat transfer coefficient on the fins are determined using the laminar flow and RNG k-ε turbulence models. More accurate results can be obtained, if the heat transfer coefficient obtained is close to the inverse results and matches existing correlations. Furthermore, the fin temperature measured at the selected locations also coincides with the experimental temperature data. The results obtained using the RNG k-ε turbulence model are more accurate than those using the laminar flow model. An interesting finding is the number of grid points may also need to change with fin spacing and air speed.

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Abbreviations

Af :

Lateral surface area of fin (m2)

Aj :

Area of the jth sub-fin region (m2)

cμ, c1ε, c2ε :

Coefficients in turbulent model, 0.0845, 1.42, 1.68

cp :

Specific heat (J/kg-K)

Dh :

Hydraulic diameter (m)

d0 :

Outer diameter of the circular tube (m)

gj :

Gravitational acceleration in xj direction (m/s2)

Gb :

Production of turbulent kinetic energy due to buoyancy, \({\text{G}}_{\text{b}} =\upbeta{\text{g}}_{\text{j}} \frac{{\upmu_{\text{t}} }}{{\Pr_{\text{t}} }}\frac{{\partial {\text{T}}_{\text{a}} }}{{\partial {\text{x}}_{\text{j}} }}\)

Gk :

Production of turbulent kinetic energy due to the velocity gradient, Gk = μtS2

h:

Local heat transfer coefficient (W/m2-K)

\({\bar{\text{h}}}\) :

Average heat transfer coefficient on the fin (W/m2-K)

\({\bar{\text{h}}}_{ 0}\) :

Heat transfer coefficient under the situation of \({\bar{\text{T}}}_{\text{o}}\) (W/m2-K)

\({\bar{\text{h}}}_{\text{j}}\) :

Heat transfer coefficient in the j-th sub-fin region (W/m2-K)

k:

Turbulent kinetic energy

kf :

Thermal conductivity of fin (W/m-K)

ka :

Thermal conductivity of air (W/m-K)

L:

Length and width of the square fin (m)

N:

Number of sub-fin regions

Ntf :

Number of grid points on the lateral surface

p:

Pressure

Pr:

Prandtl number

Prt :

Turbulent Prandtl number, 0.85

Q:

Total heat rate dissipated from the entire fin (W)

Qj :

Heat rate dissipated from the jth sub-fin region (W)

s:

Fin spacing (mm)

S:

(2 Sij Sij)1/2

Si :

Outer boundary surface of the ith circular tube

Sij :

Mean strain rate tensor, (\(\partial\) ui/ \(\partial\) xj + \(\partial\) uj/ \(\partial\) xi)/2

T:

Fin temperature (K)

Ta :

Air temperature (K)

Tj :

Measured fin temperature at the jth measurement location (K)

To,i :

Outer surface temperature of the ith circular tube (K)

\({\bar{\text{T}}}_{\text{o}}\) :

Average temperature of the four tubes (K)

T∞ :

Ambient air temperature (K)

t:

Fin thickness (m)

ui :

Velocity component in xi direction (m/s)

Vair :

Frontal air velocity (m/s)

x, y, z:

Cartesian coordinates (m)

xi :

Index notation of Cartesian coordinates (m)

αε :

Parameter in Eq. (15)

αp :

Parameter in Eq. (10)

β:

Volumetric thermal expansion coefficient

βt :

Parameter in RNG k-ε model, 0.012

δij, δj2 :

Kronecker delta function

ε:

Viscous dissipation rate of turbulence kinetic energy

η:

Ratio of characteristic time scales of turbulence and the mean flow fields, η = Sk/ε

η0 :

Parameter, 4.38

μeff :

Total dynamic viscosity, ρνeff = ρν + μt

μt :

Eddy viscosity, cμρk2/ε

ν:

Laminar kinematic viscosity (kg/s-m)

νeff :

Effective kinematic viscosity, μeff/ρ (kg/s-m)

νt :

Turbulent kinematic viscosity, μt/ρ (kg/s-m)

\(\uprho\) :

Air density (kg-m3)

σk, σε :

Turbulent Prandtl numbers for diffusion of k and ε, 1.393, 1.393

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Acknowledgments

The authors gratefully acknowledge the financial support provided by the National Science Council of the Republic of China under Grant No. NSC 98-2221-E-006-177-MY3 and NSC 102-2221-E-006-177-MY3. We would also like to thank Professor Chin-Hsiang Cheng at National Cheng Kung University for providing us access to the computational fluid dynamics software FLUENT.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Cheng Kung University, Tainan, 701, Taiwan

    Han-Taw Chen, Chih-Han Lu & Yao-Sheng Huang

  2. Department of Mechanical Engineering, Far East University, 49 Chung Hua Rd., Hsin-Shih, Tainan, 744, Taiwan

    Kuo-Chi Liu

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  1. Han-Taw Chen
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Correspondence to Han-Taw Chen.

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Chen, HT., Lu, CH., Huang, YS. et al. Numerical estimation of heat transfer characteristics for two-row plate-finned tube heat exchangers with experimental data. Heat Mass Transfer 52, 969–979 (2016). https://doi.org/10.1007/s00231-015-1612-5

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