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Table B3

Empirical correlations.

Researcher Correlation Remark
Calmidi and Mahajan [33] Developed for metal foam with porosity ranges higher than 90%
C1: depends on fluid material and
Best fit was obtained for C2 = 0.763
Ingersoll, from reference [99] Developed for moist soils. Modified version of the Series model
Dul'nev and Zarichnyak, from reference [58,100] Bhattacharya et al. [13] Dietrich et al. [101] Dul'nev and Zarichnyak: A = 3/2
Bhattacharya et al.:
A = 0.35 In [103] the intrinsic solid phase conductivity is used
Ackermann et al. [102] Developed for Reticulated Porous Ceramic (RPC)
Ackermann et al. [102] Developed for Reticulated Porous Ceramic (RPC)
Chaudhary and Bhandari, from reference [58] 0 ≤ F ≤ 1: fraction of solid in direction of the heat flow
Singh and Kasana [51] Developed for metal foams. C = 0.9683 (Air). C = 1.0647 (Water) after fitting data of [13]
Jagjiwanram and Singh [103] corrected θ: slab inclination with respect to the heat flow
Krisher [104] Packed bed of spheres. A highly anisotropic structure is assumed
Kumar et al. [105] Derived from Maxwell upper bound. Values of A and B were obtained from fitting for different materials such as rocks, polymers, and composites
Hadley [30] Developed for a consolidated mixture of two metal powders. No values of A and B for metal foams
Mendes et al. [106] Mendes et al. [107] Wulf et al. [53] dimensionless thermal conductivity depended on the presence of local material or phase. D: characteristic dimension of lumps. d: characteristic dimension of strut cross-section
Mendes et al. [108] Open-cell foam-like structures. dimensionless thermal conductivity depended on the presence of local material or phase. D: characteristic dimension of lumps. d: characteristic dimension of strut cross-section.
Where is the ETC in presence of a reference fluid with k f   = keff,rel
Fourie and Du Plessis [61] Under thermal non-equilibrium condition. kss, kff: effective thermal conductivities. kfs, ksf coupled thermal conductivities. Properties of representive unit cell varies in range of: 0.8 < ε < 0.98 and 0.0001 < kf/ks < 0.1
Coquard et al. [60] Developed for metal and ceramic foams.
Correlations obtained after fitting of numerical results for variety of unit cells (cube, dodecahedron, tetrakaidecahedron), struts (triangular, square) and lumps (cubic, parallelepipedic). D: characteristic dimension of lumps. d: characteristic dimension of strut cross-section.
Woodside and Messmer, from reference [99] Unconsolidated sands.
Krupiczka, from reference [1] Developed for packed beds of spherical particles.
Hamilton and Crosser [59] Developed for heterogeneous two-component mixtures.
Lemlich, from reference [39] Derived for the electrical conductivity of polyhedral liquid foams.
Ashby [109] Developed for cellular solids (foams and lattices).
Bhattacharya et al. [13] The best fit for all the data was found for A = 0.35
Sadeghi et al. [70] Developed for Al foams with porosity range from 0.9 to 1.

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