Research Papers: Heat and Mass Transfer

A General Expression for the Stagnant Thermal Conductivity of Stochastic and Periodic Structures

[+] Author and Article Information
X. Bai

Graduate School of Science and Technology,
Shizuoka University,
3-5-1 Johoku,
Naka-ku 432-8561, Hamamatsu, Japan

C. Hasan

Department of Mechanical Engineering,
Izmir Institute of Technology,
Urla 35430, Turkey

M. Mobedi

Faculty of Engineering,
Shizuoka University,
3-5-1 Johoku,
Naka-ku 432-8561, Hamamatsu, Japan

A. Nakayama

Faculty of Engineering,
Shizuoka University,
3-5-1 Johoku,
Naka-ku 432-8561, Hamamatsu, Japan;
School of Civil Engineering and Architecture,
Wuhan Polytechnic University,
Wuhan 430023, Hubei, China
e-mail: nakayama.akira@shizuoka.ac.jp

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received April 17, 2017; final manuscript received September 9, 2017; published online January 17, 2018. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 140(5), 052001 (Jan 17, 2018) (4 pages) Paper No: HT-17-1216; doi: 10.1115/1.4038449 History: Received April 17, 2017; Revised September 09, 2017

A general expression has been obtained to estimate thermal conductivities of both stochastic and periodic structures with high-solid thermal conductivity. An air layer partially occupied by slanted circular rods of high-thermal conductivity was considered to derive the general expression. The thermal conductivity based on this general expression was compared against that obtained from detailed three-dimensional numerical calculations. A good agreement between two sets of results substantiates the validity of the general expression for evaluating the stagnant thermal conductivity of the periodic structures. Subsequently, this expression was averaged over a hemispherical solid angle to estimate the stagnant thermal conductivity for stochastic structures such as a metal foam. The resulting expression was found identical to the one obtained by Hsu et al., Krishnan et al., and Yang and Nakayama. Thus, the general expression can be used for both stochastic and periodic structures.

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Fig. 1

Typical sandwich structure with truss core

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Fig. 2

Air layer with slanted rods

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Fig. 3

Physical model for detailed three-dimensional numerical computation

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Fig. 4

Temperature distribution obtained from three-dimensional numerical computation: (a) air phase, (b) solid phase, and (c) cross-sectional view

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Fig. 5

Polar coordinate and solid angle



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