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Effective Thermal Conductivity Modelling for Closed-Cell Porous Media with Analytical Shape Factors

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Abstract

This paper presents a fully analytical model for the effective thermal conductivity of two-phase porous media with two-/three-dimensional closed cells, applicable to honeycombs and closed-cell foams. The present model combines an existing analytical expression derived based on the Laplace heat conduction equation with an analytical shape factor which corrects the deviation caused from a non-circular (or non-spherical) pore inclusion. Results demonstrate the validity of the present model capable of analytically estimating the effective thermal conductivity of closed-cell porous media. The simple yet accurate model provides the physical mechanisms of how effective thermal conductivity depends upon the shape of pores.

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Abbreviations

\(A\) :

Area of a regular polygon (\(\hbox {m}^{2})\)

\(C\) :

Perimeter of a representative pore (m)

\(C_\mathrm{{ref}}\) :

Perimeter of a reference circular pore (m)

\(k_\mathrm{{c}} \) :

Thermal conductivity of a continuous phase (\(\hbox {W m}^{-1 }\,\hbox {K}^{-1})\)

\(k_\mathrm{{e}}\) :

Effective thermal conductivity of porous media (\(\hbox {W m}^{-1 }\,\hbox {K}^{-1})\)

\(k_\mathrm{{p}}\) :

Thermal conductivity of a discrete phase (pores) (\(\hbox {W m}^{-1 }\,\hbox {K}^{-1})\)

\(n\) :

Number of the sides of a regular polygon

\(R\) :

Radius of a reference circular pore (m)

\(S\) :

Surface area of a polyhedral pore (\(\hbox {m}^{2})\)

\(S_\mathrm{{ref}}\) :

Surface area of a reference spherical pore (\(\hbox {m}^{2})\)

\(V\) :

Total volume in a porous medium (\(\hbox {m}^{3})\)

\(V_0\) :

Total volume of an unperturbed continuous medium (\(\hbox {m}^{3})\)

\(\beta \) :

Shape factor of a representative pore

\(\beta _2\) :

Two-dimensional shape factor

\(\beta _3\) :

Three-dimensional shape factor

\(\varepsilon \) :

Porosity

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Acknowledgments

This work was supported by the National 111 Project of China (B06024), the National Basic Research Program of China (2011CB610305), the Major International Joint Research Program of China (11120101002) and the National Natural Science Foundation of China (51206128).

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Authors and Affiliations

  1. School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an,  710049, People’s Republic of China

    Xiaohu Yang

  2. State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an,  710049, People’s Republic of China

    Tianjian Lu

  3. School of Mechanical Engineering, University of the Witwatersrand, Wits, Johannesburg,  2050, South Africa

    Tongbeum Kim

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  1. Xiaohu Yang
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Correspondence to Tianjian Lu or Tongbeum Kim.

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Yang, X., Lu, T. & Kim, T. Effective Thermal Conductivity Modelling for Closed-Cell Porous Media with Analytical Shape Factors. Transp Porous Med 100, 211–224 (2013). https://doi.org/10.1007/s11242-013-0212-4

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