Open Access
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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