A general expression for the stagnant thermal conductivity of stochastic and periodic structures

[+] Author and Article Information
Xiaohui Bai

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

Celik Hasan

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

Moghtada Mobedi

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

Akira Nakayama

School of Civil Engineering and Architecture, Wuhan Polytechnic University, Wuhan, Hubei 430023, China

1Corresponding author.

ASME 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 3-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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