On the effective thermal conductivity of aluminum metal foams: Review and improvement of the available empirical and analytical models

How to Study Thermal Applications of Open-Cell Metal Foam: Experiments and Computational Fluid Dynamics

“…De Jaeger [34] has determined these effective conductivities based on his hybrid numerical model. Similar techniques for this are also discussed by Haussener et al [69] and Ranut [71]. The numerical results obtained here are also verified by the work of Le et al [70] using sound to measure the tortuosity.…”

“…For the determination of the effective properties (effective viscosity ${\mu }_e$ and both effective conductivities $\stackrel{=}{k_{f,e}}$ and $\stackrel{=}{k_{s,e}}$), the reader is referred to [34,69,70,71,72,73,74] in which these parameters are determined numerically or analytically. De Jaeger [34] has determined these effective conductivities based on his hybrid numerical model.…”

Numerical study of effective heat conductivities of foams by coupled conduction and radiation

“…Evaluation of these properties has been the subject of abundant literature, both on the experimental and modeling sides. We refer the reader to recent reviews on the subject, for instance, a very broad review of analytical and empirical models for aluminum foams [17,18].…”

“…Following very early work [26], analytical models are generally based on the simplification of a given structure into a network of thermal resistances. The foams are generally considered as saturated by a fluid; accordingly, the models depend on solid and fluid intrinsic conductivities, plus some geometrical parameters that can be as simple as just porosity, or more elaborate [18]. Many geometries have been analyzed: arrangements of cubes with or without spherical holes [27], hexagonal cells [28], fiber assemblies [29,30], symmetrical interconnected network of fibers and cavities [31] [38] extracted an equivalent resistance network from a scan and solved quasi-analytically the associated transfer problem.…”

Microscopic theory of capillary pressure hysteresis based on pore-space accessivity and radius-resolved saturation

“…In the typical case of well-connected pores, diverse physical phenomena in porous media, such as fluid flow, heat and mass transfer, gas adsorption, and phase transformations, may be amenable to homogenized macroscopic descriptions [2], although the exact connection with microscopic details of the porous medium is not always clear. Remarkably, any continuum model implicitly assumes that the overall effects of the often nontrivial pore-space morphologies [3] can be encapsulated in a small number of parameters, e.g., porosity, φ, tortuosity, τ , intrinsic permeability, k s , effective thermal conductivity, k e , etc., and the state of any fluid phase can be described by a small number of distributed state variables, e.g., pressure, p, saturation, s, etc.. For certain simple physical processes, especially those involving a single fluid phase, simple continuum formulations generally work well, and a rigorous connection between the porescale and continuum-scale governing equations can be sought -examples include single-phase flow [4,5] and heat transfer [6,7] -although estimating the transport coefficients from microscopic features of the porous medium is still an open research problem [8,9,10,11,12].…”