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An assessment of expressions for the apparent thermal conductivity of cellular materials

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Abstract

Diverse expressions for the thermal conductivity of cellular materials are reviewed. Most expressions address only the conductive contribution to heat transfer; some expressions also consider the radiative contribution. Convection is considered to be negligible for cell diameters less than 4 mm. The predicted results are compared with measured conductivities for materials ranging from fine-pore foams to coarse packaging materials. The dependencies of the predicted conductivities on the material parameters which are most open to intervention are presented graphically for the various models.

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Abbreviations

a :

Absorption coefficient

C v (Jmol−1 K−1):

Specific heat

E :

Emissivity

E L :

Emissivity of hypothetical thin parallel layer

E 0 :

Boundary surfaces emissivity

f :

Fraction of solid normal to heat flow

fics:

Fraction of total solid in struts of cell

K(m−1):

Mean extinction coefficient

k(W m−1 K−1):

Effective thermal conductivity of foam

k cd(W m−1 K−1):

Conductive contribution

k cr(W m−1 K−1):

Convective contribution

k g(W m−1 K−1):

Thermal conductivity of cell gas

k r(W m−1 K−1):

Radiative contribution

k s(W m−1 K−1):

Thermal conductivity of solid

L(m):

Thickness of sample

L g(m):

Diameter of cell

L s(m):

Cell-wall thickness

n :

Number of cell layers

r :

Reflection coefficient

t :

Transmission coefficient

T(K):

Absolute temperature

T m(K):

Mean temperature

T N :

Fraction of energy passing through cell wall

T 1(K):

Temperature of hot plate

T 2(K):

Temperature of cold plate

V g :

Volume fraction of gas

V w :

Volume fraction of total solid in the windows

w :

Refractive index

δ(m):

Effective molecular diameter

η(Pa s):

Gas viscosity

θ:

Structural angle with respect to rise direction

σ(W m−2 K−4):

Stefan constant

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  1. P. G. Collishaw

    Present address: A B B Transportation Ltd., Derby Carriage Works, Derby, UK

Authors and Affiliations

  1. Department of Materials Technology, Brunel University, UB8 3PH, Uxbridge, Middlesex, UK

    P. G. Collishaw & J. R. G. Evans

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Collishaw, P.G., Evans, J.R.G. An assessment of expressions for the apparent thermal conductivity of cellular materials. J Mater Sci 29, 486–498 (1994). https://doi.org/10.1007/BF01162512

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