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Correlation for the fin Nusselt number of natural convective heat sinks with vertically oriented plate-fins

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Abstract

In this paper, a correlation for estimating the fin Nusselt number of natural convective heat sinks with vertically oriented plate-fins is suggested. For this purpose, extensive experimental investigations are performed for various channel widths, heights and input powers. A numerical simulation is conducted by using a commercial tool to verify the present experimental results and examine fluid flow and heat transfer characteristics of a natural convective heat sink. By comparison of the present study and the previous studies, it is shown that the present correlation is widely applicable for Elenbaas numbers between 0.5 and 2 × 106 and is more accurate than previous correlations. Based on an asymptotic approach, it is found that the optimal channel width is independent of the heat sink height but dependent of the heat sink length, the difference between the heat sink base and the ambient temperatures, and fluid property.

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Abbreviations

A :

Area, m2

B :

Bias error

c f :

Heat capacity, J kg−1 K−1

El :

Elenbaas number, \( \left( { \equiv \frac{{g\beta \left( {T_{w} - T_{amb} } \right)\Pr w_{c}^{4} }}{{L\nu^{2} }}} \right) \)

g :

Gravity acceleration, m s−2

H :

Heat sink height, m

h :

Heat transfer coefficient, W m−2 K−1

k :

Thermal conductivity, W m−1 K−1

L :

Heat sink length, m

N :

Data number

n :

Correlation exponent

n fin :

Fin number

Nu :

Nusselt number

Nu r :

Average Nusselt number based on the characteristic length

P :

Precision error

Pr :

Prandtl number

q in :

Input heat to a film heater, W

q total :

Total heat transfer rate removed from a heat sink, W

Ra :

Rayleigh number

R th :

Thermal resistance, K W−1

r :

Characteristic length (=2Hw c /(2H + w c )), m

S :

Standard deviation

T :

Temperature, °C

ΔT :

Difference between the heat sink base and the ambient temperatures, °C

T 95 %,v :

t-Distribution for a confidence level of 95 %

U :

Uncertainty

W :

Heat sink width, m

w c :

Channel width, m

w w :

Fin thickness, m

β :

Volume expansion coefficient, K−1

ε :

Emissivity

η :

Fin efficiency

μ :

Viscosity, Pa s

υ:

Kinematic viscosity, m2 s−1

ρ :

Density, kg m−3

σ :

Stefan-Boltzmann constant, W m−2 K−4

amb :

Ambient

base :

Base plate

corr :

Correlation

exp :

Experiments

fin :

Fin

in :

Input

L :

Heat sink length

loss :

Heat loss

opt :

Optimum

rad :

Radiation

w :

Wall

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Acknowledgments

This work was supported by the principal research programs of the Korea Institute of Machinery and Materials (KIMM) of the republic of Korea. It was also supported by the Ajou university research fund. The authors are grateful for support.

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Authors and Affiliations

  1. Korea Institute of Machinery and Materials, Daejeon, 305-343, Republic of Korea

    Tae Hoon Kim & Kyu Hyung Do

  2. Department of Mechanical Engineering, Ajou University, Suwon, 443-749, Republic of Korea

    Dong-Kwon Kim

Authors
  1. Tae Hoon Kim
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  2. Dong-Kwon Kim
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  3. Kyu Hyung Do
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Correspondence to Kyu Hyung Do.

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Kim, T.H., Kim, DK. & Do, K.H. Correlation for the fin Nusselt number of natural convective heat sinks with vertically oriented plate-fins. Heat Mass Transfer 49, 413–425 (2013). https://doi.org/10.1007/s00231-012-1100-0

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