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Research Papers: Conduction

Generalized Correlations for Predicting Optimal Spacing of Decaying Heat Sources in a Conducting Medium

[+] Author and Article Information
Young-Jin Baik

Thermal Energy Conversion Laboratory,
Korea Institute of Energy Research,
Daejeon 305-343, Korea
e-mail: twinjin@kier.re.kr

Ich-Long Ngo

Professor
School of Mechanical Engineering,
Yeungnam University,
Gyeongsan 712-749, South Korea
e-mail: ngoichlong@ynu.ac.kr

Jang Min Park

Professor
School of Mechanical Engineering,
Yeungnam University,
Gyeongsan 712-749, South Korea
e-mail: jpark@yu.ac.kr

Chan Byon

Professor
School of Mechanical Engineering,
Yeungnam University,
Gyeongsan 712-749, South Korea
e-mail: cbyon@ynu.ac.kr

1Co-first author: Y.-J. Baik and I.-L. Ngo contributed equally to this work.

2Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 4, 2015; final manuscript received April 11, 2016; published online May 17, 2016. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 138(9), 091301 (May 17, 2016) (6 pages) Paper No: HT-15-1692; doi: 10.1115/1.4033461 History: Received November 04, 2015; Revised April 11, 2016

This paper presents a numerical study for predicting the optimal spacing (OS) of decaying heat sources/sinks in a conducting medium. The optimal configuration that minimizes the overall thermal resistance between the cylinder array and surrounding medium is tracked using interpolation technique. Consequently, the dimensionless OS obtained is of the order of 0.442th power of the Fourier number (Fo) defined as a function of the decaying time constant, which differs from the 0.5th value reported in previous study. In addition, the overall thermal resistance is shown to be highly dependent on the dimensionless spacing and Fo, while the OS also depends on the array type of the cylinders. Based on the extensive numerical study, closed-form correlations are proposed for predicting the OS of decaying heat sources/sinks in both quadratic and hexagonal arrangements. These results can be widely utilized for optimally positioning heat sources/sinks with two dimensional configurations.

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Figures

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Fig. 1

Schematic diagram of cylinder array containing heat sources

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Fig. 2

Two types of periodic cylinder arrays with constant pitch

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Fig. 3

Computational domain and boundary conditions

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Fig. 4

Comparison between present result and that from Eq.(12) at r/D = 2

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Fig. 5

Temperature distribution for various times, Fo = 0.25 and S/D = 1.2

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Fig. 6

Variation of spatial maximum temperature with time and spacing, Fo = 0.01

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Fig. 7

Variation of thermal resistance with spacing and Fo

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Fig. 8

OS as a function of Fo compared with previous data

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Fig. 9

OS for both quadratic and hexagonal arrays

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