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Table B2
Analytical models.
Researcher  Model  Remark 

Behrang et al. [37] (ParallelseriesMaxwell model) 
S_{w}
: wetting phase saturation K: thermal conductivity Δ: volume fraction ε: Porosity 

Bhattacharya et al. [13] 
r: half thickness of fiber L: halflength of fiber 

Yao et al. [82] 
a_{2}: geometrical parameter controlling crosssectional size of ligament L: distance between centers of neighboring nodes 

Gong et al. [83]  In this theory, phases (or components) are treated as small spheres dispersing into an assumed uniform medium with the thermal conductivity km. m: uniform medium with dispersed spheres. e: two components system 

Kou et al. [38]  Fractal dimensions D_{f}
, D_{t}
, and D_{f,w}
(or D_{f,g}
) ʎ: Pore size 

Bhattacharya [84] circular lump corrected  Developed for metal foams. 2D array of hexagonal cells, with hexagonal lumps of metal at fibers' intersection. Four layers in series 

Boomsma and Poulikakos [32], revised  Developed for metal foams. 3D tetrakaidecahedron, struts of cylindrical cross section, with cubic nodes at fibres' intersection. Four layers in series. The parameter e must be estimated from data fitting. r: lump thickness L: strut length d: strut radius 

Dai et al. [34]  Developed for metal foams. Improvement of the above model. Accounts for struts' orientation Φ = 45^{∘} Good predictions but with an unfeasible value of e/r 

Yang et al. [85]  Developed for metal foams. Improvement of the acove model; considers the variation of e with porosity a_{0},a_{1},a_{2},a_{3} calibrated against data of [32]: valid for 0.905 < ε < 0.978 

Yang et al. [86]  Developed for metal foams. 1/16th of a tetrakaidecahedron unit cell. No lumps at ligaments' intersection. The coefficient 1/3 is the reciprocal of thermal tortuosity. The same form of the Lemlich model is obtained 

Yang et al. [11] 
Accounting for the variation of struts'cross section: 
1/16 th 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 crosssectional area ratio e ≥ 0: node thickness to strut length ratio φ: ratio of ligament crosssectional area in the middle to that at the end 
Kumar and Topin [87]  Developed for metal foams. F is fraction of material oriented in heat flow direction 

Kumar and Topin [87] PF model  Developed for metal foams. Γ is defined as resistor model. Valid for 0.6 < ε < 0.95 

Dul'nev and Novikov [88]  
Hsu et al. [89] touching square cylinders  2 Dimensional l: length of one side of solid square cylinder 

Hsu et al. [89] touching cubes  3 Dimensional l: length of one side of cube 

Wang et al. [90]  Efficient for all ranges of porosities and hollow or solid struts  
Singh et al. [91] spherical inclusions 
n
^{'}: fractional volume of the more highly conducting phase a/b: node to cell size ratio 

Singh et al. [91] cubic inclusions 
n
^{'}: fractional volume of the more highly conducting phase and a/b is node to cell size ratio C_{1} and C_{2}: constants 

Jagjiwanram and Singh [92] ellipsoidal inclusion  n ^{′}: fractional volume of the more highly conducting phase and a/b is node to cell size ratio  
Zehner and Schundler, from Ref. [36] 
n is shape factor and at n = 1 solid becomes sphere k_{ r } = k_{ f }/k_{ s }: fluid/solid thermal conductivity ratio 

Hsu et al. [36] Area contact model 
n is shape factor and at n = 1 solid becomes sphere k_{ r } = k_{ f }/k_{ s }: fluid/solid thermal conductivity ratio α: deformation factor 

Hsu et al. [36] Phasesymmetry model 
n is shape factor and at n = 1 solid becomes sphere k_{ r } = k_{ f }/k_{ s } : fluid/solid thermal conductivity ratio α: deformation factor 

Russel, from Ref. [58]  pores are cubes of the same size with solid walls of uniform thickness  
Ahern et al. [93]  : the fraction of solid material contained in the windows and β declares strut shapes : β = 1/3 for cylindrical struts and β = 2/3 for the platelike windows  
Schuetz and Glicksmann, from Ref. [93]  β = 1/3 for cylindrical struts and β = 2/3 for the platelike windows  
Fiedler et al. [94]  Determining ETC based on relative density of solid  
Singh et al. [95]  In order to take into accouter the random distribution of cells in the continuous matrix as well as the wide difference in the thermal conductivity of the constituents, a nonlinear secondorder correction term is correlated 

Donea Variational Model from Ref. [96] 
r: radius of inclusion, r ^{'}:radius of the largest possible spherical shell surrounding the inc!iision for random dispersion of spheres 

Bauer [97]  Compatible with experimental data obtained from wide range of thermal conductivity, pore shape and distribution k_{0}: thermal conductivity of unperturbed continuous medium  
Kuwahara et al. [98]  Analytical correlation established for air and aluminium as fluid and sold phases under nonequilibrum thermal condition 
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