The effective stagnant thermal conductivity of porous media with periodic structures

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 ape discussed. Comparisons of the analytical expressions with numerical solutions and experimental data are made whenever possible.