ISSN 打印: 1091-028X
ISSN 在线: 1934-0508

# 多孔介质期刊

DOI: 10.1615/JPorMedia.v2.i1.20
pages 19-38

## The Effective Stagnant Thermal Conductivity of Porous Media with Periodic Structures

Ping Cheng
Mechanical Engineering Department, The Hong Kong University of Science and Technology; MOE Key Laboratory for Power Machinery and Engineering, School of Mechanical and Power Engineering, Shanghai Jiao Tong University, Shanghai 200240, P. R. China
Chin-Tsau Hsu
Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

### ABSTRACT

Existing analytical models for predicting the effective stagnant thermal conductivity of fluid-saturated spatially periodic media are summarized. These include the analytical solutions given by Maxwell (1873) and Rayleigh (1892), and the early models proposed by Deissler and Eian (1952), Kunii and Smith (1960), and Zehner and Schlunder (1970). Recent models such as the area-contact model, the phase-symmetry model, the single-scale lumped parameter model, and the multiscale lumped parameter model are emphasized. Simple algebraic expressions for the effective stagnant thermal conductivity of a number of geometries based on these recent models are presented. These include two-dimensional geometries such as square, circular, and elliptic cylinders and composite materials consisting of fiber bundles, as well as three-dimensional geometries such as ellipsoids, cubes, and wire screens. The effects of porosity, shape, and arrangement of the solid phases, as well as the solid-to-fluid thermal conductivity ratio are illustrated. The effects of point and finite contacts between the solid phase on the effective thermal conductivity of the porous medium are discussed. Comparisons of the analytical expressions with numerical solutions and experimental data are made whenever possible.

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