Similarity rule between heat transfer and pressure drop of porous materials

Abstract

Porous materials are used for many engineering components such as the fixed bed for chemical reactors, the regenerator of the Stirling engine, and the pebble bed of the high-temperature gas-cooled nuclear reactor.In general, the heat-transfer and pressure-drop characteristics of porous materials cannot be easily specified, except for the fixed beds of uciform, simply-shaped particles of spheres and cylindrical beads. For these simple particles, the characteristic length is usually defined by the diameter d or 6V/S, which characterizes the heat-transfer and/or pressure-drop properties. However, it is difficult to define it for the porous materials of complex matrices such as foamed metal, fixed beds of nonuniform, and irregularly shaped particles. Thus, for porous materials without sufficient knowledge of its fine structures, experiments are carried out to get information on heat-transfer and/or pressure-drop characteristics. The purpose of this work is to predict the heat-transfer characteristics from the pressure drop data, since heat-transfer experiments are much more difficult.Much research has been carried out on heat-transfer (Dhingra, 1984;Dixon, 1979;Kudra, 1989) or on pressure-drop characteristics of porous materials (Comite, 1989;Burke, 1928;Ergun, 1949). However, studies that deal with both heat-transfer and pressure-drop characteristics simultaneously are rather scarce. Hamaguchi (1983) adopted mean bore diameter as the characteristic length of the porous metal for pressure drop and mean fiber diameter for heat transfer to yield fairly good correlations. If this choice of characteristic lengths is the best and no other alternative exists, no similarity rule is expected since the bore diameter and the fiber diameter are independent of each other. Unfortunately, Hamaguchi's (1983) experiments are not broad enough to determine the possibility of the existence of the similarity rule. Chiou (1966) tried to define the characteristic length from the pressure-drop data to correlate the heat-transfer data. This is very similar to our approach; however, his results do not seem to be good due to the improper choice of the characteristic length, as will be discussed later.Correspondence concerning this work should be directed to K. Fukuda. T. Kondoh is currently at the Toa University, Shirnonoseki 751, Japan; S. Hasegawa at the Kurume College of Technology, Kururne 830, Japan.This work shows that a proper characteristic length is determined by defining the Reynolds number Re and the Nusselt number Nu. Then a universal law or a similarity rule Nu = f ( R e ) applicable to various porous materials is derived.

The thermal state and the heat transfer in a porous metal shell upon penetration cooling

“…In Fig. 4, line 9 is also plotted, which is calculated according to the interpolation dependence proposed in [15] that generalizes numerous experimental data on air for globules, cylindrical particles, meshed mate rials, and other porous media obtained mainly in Japan with accuracy ±40%:…”