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The Simplified Analytical Models for Evaluating the Heat Transfer Performance of High-Porosity Metal Foams

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Abstract

The accurate evaluation of the specific surface area and the effective thermal conductivity (ETC) of high-porosity metal foams is an important prerequisite to study the mechanism of heat transfer enhancement. In this paper, the tetrakaidecahedron, concave triangular prism and equivalent tetrahedron were used to develop the geometry shapes of cell, ligament and node, respectively. The calculation model of the specific surface area characterized by porosity and pore density (PPI) was deduced by considering the shape characteristics. Based on the angle between the two-dimensional plane skeleton layer and the heat flow direction, the ETC analytical calculation model characterized by only the porosity in the three-dimensional space was deduced. Without any other fitting or experimental empirical parameters, these two models are only related to porosity and PPI, which are the most readily available parameters for the metal foams. The results of these models are consistent with the experimental and empirical data in other literature, indicating that these models are both versatile and accurate.

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Abbreviations

S v :

Specific surface area (m−1)

φ :

Porosity

\( d_{s} \) :

Ligament thickness \( \left( {\text{m}} \right) \)

\( d_{w} \) :

Cell pore diameter \( \left( {\text{m}} \right) \)

\( l \) :

Length of the ligament \( \left( {\text{m}} \right) \)

\( a_{1} \) :

Parameter that affects the shape of the ligament cross section

\( a_{2} \) :

Height of the pyramid \( \left( {\text{m}} \right) \)

\( a_{3} \) :

Parameter that controls the shape of the ligament along the axial direction

\( V \) :

Volume \( \left( {{\text{m}}^{3} } \right) \)

\( S \) :

Surface area \( \left( {{\text{m}}^{2} } \right) \)

\( d_{r} \) :

Inscribed circle diameter of cell \( \left( {\text{m}} \right) \)

\( k \) :

Thermal conductivity \( \left( {{\text{W}} \cdot {\text{m}}^{ - 1} \cdot {\text{K}}^{ - 1} } \right) \)

PPI:

Pore number per inch

\( \Delta T \) :

Temperature difference \( \left( {\text{K}} \right) \)

\( Q \) :

Heat \( \left( {\text{J}} \right) \)

A, B, C:

Serial number of plane skeleton layer

\( H \) :

Height of cell \( \left( {\text{m}} \right) \)

\( A_{l} \) :

Cross-sectional area of ligament \( \left( {{\text{m}}^{2} } \right) \)

\( A_{b} \) :

Bottom area of cell \( \left( {{\text{m}}^{2} } \right) \)

λ :

Parameter, \( \lambda = a_{2} /l \)

α :

Angle

l :

Ligament

n :

Node

cell :

Cell

foam :

Metal foams

max :

Maximum

min :

Minimum

s :

Solid phase

f :

Fluid phase

hex :

Hexahedron

e :

Effective

t :

Total

p :

Plane skeleton layer

References

  1. P.S. Liu, Philos. Mag. Lett. 90, 447–453 (2010)

    Article  ADS  Google Scholar 

  2. M. Lacroix, P. Nguyen, D. Schweich, C.P. Huu, S. Savin-Poncet, D. Edouard, Chem. Eng. Sci. 62, 3259–3267 (2007)

    Article  Google Scholar 

  3. A. Inayat, H. Freund, T. Zeiser, Chem. Eng. Sci. 66, 1179–1188 (2011)

    Article  Google Scholar 

  4. F.C. Buciuman, B. Kraushaarczarnetzki, Ind. Eng. Chem. Res. 42, 1863–1869 (2003)

    Article  Google Scholar 

  5. J. Grosse, B. Dietrich, G.I. Garrido, P. Habisreuther, N. Zarzalis, H. Martin, M. Kind, B. Kraushaar-Czarnetzki, Ind. Eng. Chem. Res. 48, 10395–10401 (2009)

    Article  Google Scholar 

  6. D.L. Duan, R.L. Zhang, X.J. Ding, S. Li, Mater. Sci. Technol. 22, 1364–1367 (2006)

    Article  Google Scholar 

  7. V.V. Calmidi, R.L. Mahajan, J. Heat Trans-T ASME 121, 466–471 (1999)

    Article  Google Scholar 

  8. A. Bhattacharya, V.V. Calmidi, R.L. Mahajan, Int. J. Heat Mass Transfer 45, 1017–1031 (2002)

    Article  Google Scholar 

  9. L.J. Gibson, M.F. Ashby, Cellular Solids: Structure and Properties, vol. 33 (Cambridge University Press, Cambridge, 1988), pp. 487–488

    MATH  Google Scholar 

  10. K. Boomsma, D. Poulikakos, Int. J. Heat Mass Transf. 44, 827–836 (2001)

    Article  Google Scholar 

  11. Z. Dai, K. Nawaz, Y.G. Park, J. Bock, A.M. Jacobi, Int. Commun. Heat Mass 37, 575–580 (2010)

    Article  Google Scholar 

  12. S. Kanaun, O. Tkachenko, Int. J. Eng. Sci. 46, 551–571 (2008)

    Article  Google Scholar 

  13. Y. Yao, H. Wu, Z. Liu, Int. J. Therm. Sci. 97, 56–67 (2015)

    Article  Google Scholar 

  14. W. Thomson, Acta Math. 11, 121–134 (1887)

    Article  MathSciNet  Google Scholar 

  15. Jagjiwanram, R. Singh, Appl. Therm. Eng. 24, 2727–2735 (2004)

    Article  Google Scholar 

  16. M.S. Phanikumar, R.L. Mahajan, Int. J. Heat Mass Transf. 45, 3781–3793 (2002)

    Article  Google Scholar 

  17. E. Sadeghi, S. Hsieh, M. Bahrami, J. Phys. D Appl. Phys. 44, 125406 (2009)

    Article  ADS  Google Scholar 

  18. J.W. Paek, B.H. Kang, S.Y. Kim, J.M. Hyun, Int. J. Thermophys. 21, 453–464 (2000)

    Article  Google Scholar 

  19. X.H. Yang, J.J. Kuang, J.X. Bai, T.J. Lu, D.F. Jin, J. Xi’an Jiao Tong Univ. 48, 79–84 (2014)

    Google Scholar 

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Acknowledgment

This work was supported by National Basic Research Program of China-973 Program 2015CB857100.

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Authors and Affiliations

  1. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Hangming Shen, Qian Ye & Guoxiang Meng

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  1. Hangming Shen
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  2. Qian Ye
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  3. Guoxiang Meng
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Correspondence to Qian Ye.

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Shen, H., Ye, Q. & Meng, G. The Simplified Analytical Models for Evaluating the Heat Transfer Performance of High-Porosity Metal Foams. Int J Thermophys 39, 87 (2018). https://doi.org/10.1007/s10765-018-2405-0

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