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Table B4

Unit cell models ETCs of open-cell metal foams.

Researcher Unit cell Correlation Remarks
Calmidi and Mahajan [33] Two-dimensional hexagonal array square nodes fibers are the edges of the hexagons one dimensional conduction
: ligament to node size ratio representative unit cell:

Divided into three layers in series formation and parallel law is would be applied for each separate layer
Bhattacharyaet al. [13] –Six-fold rotational symmetry
–Circular cross sction representative unit cell:

Divided into 5 layers in series and in each layer fluid and solid phases would be in parallel formation.
R: radius of circular intersection
Du Plessis and Fourie [110] Representative unit cell was used to study hydrodynamic features of cellular structures. Three joint square ducts each square oriented perpendicularly to the other two sections are required to exhibit maximum possible interconnectivity.
Dulnev [111] L: outside diamension of the unit cell
Also was used to examine Odelovski correlation
Boomsma and Poulikakos [32] The tetrakaidecahedron modeled with cylindrical ligaments and cubic nodes.
d: dimensionless foam ligaments radius
e: dimensionless cubic node length representative unit cell
Schimierer and Razani [69] Three-dimensional geometric model of open celled Doucell foam
Spherical nodes with the TetraK model ligament cross section is circular and the diameter is constant over its length
kst: thermal conductivity of 304 stainless steel
Ac: cross sectional area
L: length between thermocouple locations
5 thermocouple were used (1,2,3,4,5)
Ozmat et al. [112] NA Structure of metal foam and dodecahedron having 12 pentagon-shaped facets
Krishnan et al. [113] Body center cubic
Face center cubic
A15 arrangement
ETC was calculated numerically by solving conduction heat transfer
Unit cell geometries were obtained by substracting the cell cube from spheres at various lattice points
Convex triangular ligaments cross sectional area
Symmetric tetrahedral nodes
Rayleigh models from [114] Spherical particles arranged in simple cubic array embedded in a continuous matrix
Rayleigh models from [114] Consisting of parallel cylinders embedded in a continuous matrix
Assuming z is the axis parallel to the fibers
Percolation model [114]   High-conductivity particles are depicted as black. White is for low-conductivity particles
Yang et al. [86] An open-cell Al foam modeled with a tetrakaidecahedron unit cell having a uniform thickness of square ligaments
Yang et al. [11] Accounting for the variation of struts 'cross section:
1/16th of a tetrakaidecahedron unit cell. Cubic nodes at ligaments' intersection. From experimental measurements on SEM images for Al foams: e = 0.3 and α = 1.5. α ≥ 1: node to ligament cross-sectional area ratio Page 37 of 77 e ≥ 0: node thickness to strut length ratio h: ratio of ligament cross-sectional area in the middle to end
Haghighi and Kasiri [44] Unit cell is discretized to five parallel layers in the y direction
The ligaments of all quadrilateral faces are laid between two adjacent cells
Each node at the fiber intersections is common between two cellsk is the summation of the effective thermal conductivity of each layer in series
L: ligament length
Θ: The inclination angle that defines the orientation of the hexagonal faces with respect to the rise direction
l: Length of the sides of
horizontal square faces
e: Dimensionless spherical node diameter
Talukar et al [115] A Cartesian coordinate based finite volume method (FVM) has been used for solving the combined conduction-radiation problem inside porous media.
porosity is uniform within the porous matrix the thermo-physical properties of the solid as well as the fluid (participating media) in the pores are constant over the range of temperature encountered in the simulation,
These porous structures have been assumed to be regularly repeating in all the three directions
The representative computational domain of the porous medium has been divided into a number of control volumes (CVs); each of which can be designated either as the solid or the fluid (void) control volume
Yao et al. [82] a1: geometrical parameter controlling cross-sectional shape of ligament
a2 geometrical parameter controlling cross-sectional size of ligament
L: ligament length
Edouardo [45,46] Consist of 12 cylindrical ligaments and 8 cubic nodes
2b: strut diameter and 2x: cubic node length
Huu et al. [47] NA -
Cubic cell lattice [4850] NA Cell size is equal to cubic lattices
Yu et al. [116] Cubic unit cell model for porous carbon foam
t: is the normalized thickness of the square bar

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