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Geometric models are used to simplify the complex, three-dimensional geometry of metal foams for calculations of effective thermal conductivity. The first is based on a conventional three-dimensional cubic lattice and the second is a tetrakaidecahedronal model. The models consist of interconnecting ligaments with a spherical node at their intersections. The geometry of the foam is determined based on two dimensionless parameters: 1) the porosity and 2) the product of the specific surface area of the foam and the length of the interconnecting ligaments. A free parameter represents the size of the lumps at the ligament interconnections. It is shown that the remaining unknown geometric parameters of the models can be obtained as a solution of a cubic equation that has only one acceptable solution. From the cubic lattice model, a one-dimensional heat conduction analytical model is used to find the effective thermal conductivity of fully saturated metal foam. A three-dimensional finite element calculation of the effective thermal conductivity for the cubic lattice is then compared to the one-dimensional model. In the case of the tetrakaidecahedronal model, a similar three-dimensional finite element calculation is performed to find the effective thermal conductivity. Anisotropy of the models is explored. The results of the models are compared with experimental results from this study and the literature to substantiate their accuracy. The experimental results are reported for fully saturated aluminum metal foam in air, water, and oil. Results show that both the cubic lattice model, which is less complex, and the tetrakaidecahedronal model can both be used to represent one-dimensional effective thermal conductivity. Finally, the dimensionless surface areas for each geometric model are compared. The models produce significantly different surface areas, and therefore do not both represent the density and specific surface area of foam accurately.Copyright © 2004 by ASME |
