Lattice Monte Carlo Analysis of Thermal Diffusion in Multi-Phase Materials

  • T. FiedlerEmail author
  • I. V. Belova
  • A. Öchsner
  • G. E. Murch
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 2)


This Chapter addresses the numerical simulation of thermal diffusion in multi-phase materials. A Lattice Monte Carlo method is used in the analysis of two- and three-dimensional calculation models. The composites considered are assembled by two or three phases, each exhibiting different thermal conductivities. First, a random distribution of phases is considered and the dependence of the effective thermal conductivity on the phase composition is investigated. The second part of this analysis uses a random-growth algorithm that simulates the influence of surface energy on the formation of composite materials. The effective thermal conductivity of these structures is investigated and compared to random structures. The final part of the Chapter addresses percolation analyses. It is shown that the simulation of surface energy distinctly affects the percolation behavior and therefore the thermal properties of composite materials.


Percolation Threshold Effective Thermal Conductivity Phase Fraction Conductivity Ratio Effective Medium Theory 
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  1. 1.
    University of Magdeburg, Lab of Scanning Microscopy and StereologyGoogle Scholar
  2. 2.
    Tarnawski, V.R., Cleland, D.J., Corasaniti, S., et al.: Extension of soil thermal conductivity models to frozen meats with low and high fat content. Int. J. Refrig. 28, 840–850 (2005)CrossRefGoogle Scholar
  3. 3.
    Carson, J.K., Lovatt, S.J., Tanner, D.J., Cleland, A.C.: Predicting the effective thermal conductivity of unfrozen, porous foods. J. Food Eng. 75, 297–307 (2006)CrossRefGoogle Scholar
  4. 4.
    Sharma, A., Tyagi, V.V., Chen, C.R., Buddhi, D.: Review on thermal energy storage with phase change materials and applications. Renew. Sustain. Energy Rev. 13, 318–345 (2009)CrossRefGoogle Scholar
  5. 5.
    Fiedler, T., Öchsner, A., Belova, I.V., Murch, G.E.: Thermal conductivity enhancement of compact heat sinks using cellular metals. Defect Diffus. Forum 273–276, 222–226 (2008)CrossRefGoogle Scholar
  6. 6.
    Landauer, R.: The electrical resistance of binary metallic mixtures. J. Appl. Phys. 23, 779–784 (1952)CrossRefGoogle Scholar
  7. 7.
    Ben-Amoz, M.: The effective thermal properties of two phase solids. Int. J. Eng. Sci. 8, 39–47 (1970)CrossRefGoogle Scholar
  8. 8.
    Glatzmaier, G.C., Ramirez, W.F.: Use of volume averaging for the modelling of thermal properties of porous materials. Chem. Eng. Sci. 43, 3157–3169 (1988)CrossRefGoogle Scholar
  9. 9.
    Rio, J.A., Zimmerman, R.W., Dawe, R.A.: Formula for the conductivity of a two-component material based on the reciprocity theorem. Solid State Commun. 106, 183–186 (1998)CrossRefGoogle Scholar
  10. 10.
    Samantray, P.K., Karthikeyan, P., Reddy, K.S.: Estimating effective thermal conductivity of two-phase materials. Int. J. Heat Mass Transf. 49, 4209–4219 (2006)CrossRefGoogle Scholar
  11. 11.
    Karthikeyan, P., Reddy, K.S.: Effective conductivity estimation of binary metallic mixtures. Int. J. Therm. Sci. 46, 419–425 (2006)CrossRefGoogle Scholar
  12. 12.
    Wang, M., Pan, N., Wang, J., Chen, S.: Mesoscopic simulations of phase distribution effects on the effective thermal conductivity of microgranular porous media. J. Colloid Interface Sci. 311, 562–570 (2007)CrossRefGoogle Scholar
  13. 13.
    Wang, M., Pan, N.: Predictions of effective physical properties of complex multiphase materials. Mater. Sci. Eng. R 63, 1–30 (2008)CrossRefGoogle Scholar
  14. 14.
    Belova, I.V., Murch, G.E., Fiedler, T., Öchsner, A.: The Lattice Monte Carlo method for solving phenomenological mass and heat transport problems. Defect Diffus. Forum 279, 13–22 (2008)CrossRefGoogle Scholar
  15. 15.
    Fiedler, T., Öchsner, A., Belova, I.V., Murch, G.E.: Calculations of the effective thermal conductivity in a model of syntactic metallic hollow sphere structures using a Lattice Monte Carlo method. Defect Diffus. Forum 273–276, 216–221 (2008)CrossRefGoogle Scholar
  16. 16.
    Fiedler, T., Öchsner, A., Belova, I.V., Murch, G.E.: Recent advances in the prediction of the thermal properties of syntactic metallic hollow sphere structures. Adv. Eng. Mater. 10, 269–273 (2008)CrossRefGoogle Scholar
  17. 17.
    Fiedler, T., Solórzano, E., Garcia-Moreno, F., Öchsner, A., Belova, I.V., Murch, G.E.: Lattice Monte Carlo and experimental analyses of the thermal conductivity of random shaped cellular aluminium. Adv. Eng. Mater. (2008, submitted for publication)Google Scholar
  18. 18.
    Fiedler, T., Belova, I.V., Öchsner, A., Murch, G.E.: Non-linear calculations of transient thermal conduction in composite materials. Comput. Mater. Sci. 45, 434–438 (2009)CrossRefGoogle Scholar
  19. 19.
    Fiedler, T., Belova, I.V., Öchsner A., Murch G.E.: A Lattice Monte Carlo Analysis of Thermal Transport in Phase Change Materials. Defect Diffus. Forum 297–301, 154–161 (2010)Google Scholar
  20. 20.
    Newman, M.E.J., Ziff, R.M., Zia, R.K.P.: Two-dimensional polymer networks near percolation. J. Phys. A Math. Theor. 41, 1–7 (2008)Google Scholar
  21. 21.
    Jiří, Š., Nezbeda, I.: Percolation threshold parameters of fluids. Phys. Rev. E 79, 041141–041147 (2009)CrossRefGoogle Scholar
  22. 22.
    Bruggeman, D.A.G.: Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen. Ann. Phys. (Berlin) 416, 665–679 (1935)CrossRefGoogle Scholar
  23. 23.
    Moleko, L.K., Allnatt, A.R., Allnatt, E.L.: A self-consistent theory of matter transport in a random lattice gas and some simulation results. Philos. Mag. A 59, 141–160 (1989)CrossRefGoogle Scholar
  24. 24.
    Fiedler, T., Pesetskaya, E., Öchsner, A., Grácio, J.: Numerical and analytical calculation of the orthotropic heat transfer properties of fibre-reinforced materials. Mater. Sci. Eng. 36, 602–607 (2005)Google Scholar
  25. 25.
    Kikuchi, R.: Concept of the long-range order in percolation problems. J. Chem. Phys. 53, 2713–2718 (1970)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • T. Fiedler
    • 1
    Email author
  • I. V. Belova
    • 1
  • A. Öchsner
    • 2
    • 1
  • G. E. Murch
    • 1
  1. 1.The University of NewcastleCallaghanAustralia
  2. 2.Technical University of MalaysiaJohorMalaysia

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