Advertisement

Journal of Materials Science

, Volume 53, Issue 17, pp 12534–12542 | Cite as

A new non-contact optical method for determining the thermal conductivity of metals and carbides at their melting/freezing temperatures

  • Anatoliy I. Fisenko
  • Vladimir F. Lemberg
Metals

Abstract

It is now recognized that the contact methods to measure a thermal conductivity of metals and carbides in liquid/solid phase transition are facing some difficulties. On the other side, the normal spectral emissivity for these materials at melting/freezing points can be measured with high degree of accuracy. Therefore, it is of considerable interest to develop a method that makes it possible to determine the thermal conductivity through the measured value of the normal spectral emissivity. A new optical non-contact method to determine the thermal conductivity of metals and carbides at their melting/freezing points is proposed. This method is based on the use of the Drude model, the Hagen–Rubens relation, and the Wiedemann–Franz law. To define the thermal conductivity of materials at melting/freezing points, the experimental measurements of the normal spectral emissivity in a specific far-infrared range are needed. The proposed method does not require to model the power balance of heat transport for calculating the thermal conductivity. The applicability of the proposed method was demonstrated on cobalt, nickel, and zirconium carbide. A good agreement with experimental data published in the literature is obtained. The gap between the thermal conductivity of the materials under study in the solid and liquid phases at their melting/freezing temperatures is calculated. The temperature dependence of the thermal conductivity of the “ideal” solar power emitter is obtained.

Notes

Acknowledgements

The authors cordially thank Professor L.A. Bulavin and Professor N.P. Malomuzh for fruitful discussion.

References

  1. 1.
    Tritt TM, Weston D (2004) Measurement techniques and considerations for determining thermal conductivity of bulk materials. In: Tritt TM (ed) thermal conductivity. Springer, Boston, pp 187–203CrossRefGoogle Scholar
  2. 2.
    Shinde SL, Goela J (eds) (2006) High thermal conductivity materials. Springer, New YorkGoogle Scholar
  3. 3.
    Hamilton RL, Crosser OK (1962) Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam 1(3):187–191CrossRefGoogle Scholar
  4. 4.
    Zeller RC, Pohl RO (1971) Thermal conductivity and specific heat of noncrystalline solids. Phys Rev B 4(6):2029–2041CrossRefGoogle Scholar
  5. 5.
    Cooper MG, Mikic BB, Yovanovich MM (1969) Thermal contact conductance. Int J Heat Mass Transf 12(3):279–300CrossRefGoogle Scholar
  6. 6.
    Madhusudana CV, Fletcher LS (1986) Contact heat transfer: the last decade. AIAA J 24(3):510–523CrossRefGoogle Scholar
  7. 7.
    Prasher R (2006) Thermal interface materials: historical perspective, status, and future directions. Proc IEEE 94(8):1571–1586CrossRefGoogle Scholar
  8. 8.
    Lan R, Endo R, Kuwahara M, Kobayashi Y, Susa M (2010) Thermal conductivity measurements of solid Sb2Te3 by hot-strip method. Jpn J Appl Phys 49(7R):078003CrossRefGoogle Scholar
  9. 9.
    Yamasue E, Susa M, Fukuyama H, Nagata K (2003) Deviation from Wiedemann–Franz law for the thermal conductivity of liquid tin and lead at elevated temperature. Int J Thermophys 24:713–730CrossRefGoogle Scholar
  10. 10.
    Hisano K (1997) An apparatus for noncontact measurement of thermal conductivity by thermal radiation heating. Int J Thermophys 18(2):535–545CrossRefGoogle Scholar
  11. 11.
    Kobatake H, Fukuyama H, Minato I (2007) Noncontact measurement of thermal conductivity of liquid silicon in a static magnetic field. Appl Phys Lett 90:094102CrossRefGoogle Scholar
  12. 12.
    Manara D, De Bruycker F, Sengupta AK, Agarwal R, Kamath HS (2012) The actinide carbides. In: Konings RJM (ed) Comprehensive nuclear materials. Elsevier, Amsterdam, pp 87–137CrossRefGoogle Scholar
  13. 13.
    Manara D, De Bruycker F, Boboridis K, Tougait O, Eloirdi R, Malki M (2012) High temperature radiance spectroscopy measurements of solid and liquid uranium and plutonium carbides. J Nucl Mater 426:126–138CrossRefGoogle Scholar
  14. 14.
    Manara D, Jackson HF, Perinetti-Casoni C, Boboridis K, Welland MJ, Luzzi L, Ossi PM, Lee WE (2013) The ZrC–C eutectic structure and melting behavior: a high-temperature radiance spectroscopy study. J Eur Ceram Soc 33:134–161CrossRefGoogle Scholar
  15. 15.
    Watanabe H, Susa M, Fukuyama H, Nagata K (2003) Phase dependence (liquid/solid) of normal spectral emissivities of noble metals at melting points. Int J Thermophys 24:223–237CrossRefGoogle Scholar
  16. 16.
    Watanabe H, Susa M, Fukuyama H, Nagata K (2003) Phase (liquid/solid) and wavelength dependence of spectral emissivity for Cu, Ag, and Au at melting points in near infrared region. Int J Thermophys 24:1105–1120CrossRefGoogle Scholar
  17. 17.
    Watanabe H, Susa M, Fukuyama H, Nagata K (2003) Phase (liquid/solid) dependence of the normal spectral emissivity for iron, cobalt, and nickel at melting points. Int J Thermophys 24:473–488CrossRefGoogle Scholar
  18. 18.
    Tritt T (2004) Thermal conductivity: theory, properties, and applications. Kluwer Academic, New YorkCrossRefGoogle Scholar
  19. 19.
    Rosenberg HM (1988) The solid state: an introduction to the physics of crystals for students of physics, materials science, and engineering, 3rd edn. Oxford physics series. Oxford University Press, OxfordGoogle Scholar
  20. 20.
    Modest MF (2013) Radiative heat transfer, 3rd edn. Academic Press, CambridgeGoogle Scholar
  21. 21.
    Landau LD, Lifshitz EM (1980) Statistical physics, course of theoretical physics, vol 5. Pergamon Press, OxfordGoogle Scholar
  22. 22.
    Fisenko AI, Lemberg VF (2016) Black-body radiative, thermodynamic, and chromatic functions: tables in finite spectral ranges. Springer, BerlinCrossRefGoogle Scholar
  23. 23.
    Abramowitz M, Stegun IA (1972) Handbook of mathematical functions with formulas, graphs, and mathematical tables. Dover Publications, New YorkGoogle Scholar
  24. 24.
    Fisenko AI, Lemberg V (2015) Polylogarithmic representation of radiative and thermodynamic properties of thermal radiation in a given spectral range: II. Real-body radiation. Int J Thermophys 36:2705–2719CrossRefGoogle Scholar
  25. 25.
    Assael MJ, Antoniadis KD, Wakeham WA, Huber ML, Fukuyama H (2017) Reference correlations for the thermal conductivity of liquid bismuth, cobalt, germanium and silicon. J Phys Chem Ref Data 46(3):033101.  https://doi.org/10.1063/1.4991518 CrossRefGoogle Scholar
  26. 26.
    Nishi T, Shibata H, Ohta H (2003) Thermal diffusivity and conductivity of molten germanium and silicon. Mater Trans 44:2369–2374CrossRefGoogle Scholar
  27. 27.
    Ostrovskii OI, Ermachenkov VA, Popov VM, Grigoryan VA, Kogan LB (1980) Thermophysical properties of molten iron, cobalt, and nickel. Russ J Phys Chem 54:739–744Google Scholar
  28. 28.
    Zinovyev VY, Polev VF, Taluts SG, Zinovyeva GP, Ilinykh SA (1986) Diffusivity and thermal conductivity of 3 d-transition metals in solid and liquid states. Phys Met Metallogr 61:85–91Google Scholar
  29. 29.
    Assael MJ, Chatzimichailidis A, Antoniadis KD, Wakeham WA, Huber ML, Fukuyama H (2017) Reference correlations for the thermal conductivity of liquid copper, gallium, indium, iron, lead, nickel and tin. High Temp High Press 46(6):391–416Google Scholar
  30. 30.
    Kobatake H., Khosroabadi H., Fukuyama H (2010) Noncontact measurement of normal spectral emissivity, heat capacity and thermal conductivity of liquid Ni in a dc magnetic field. In: Proceedings of eTherm, pp 122–124Google Scholar
  31. 31.
    Nishi T, Shibata H, Ohta H, Waseda Y (2003) Thermal conductivities of molten iron, cobalt, and nickel by laser flash method. Metall Mater Trans A 34A:2801–2807CrossRefGoogle Scholar
  32. 32.
    Zapadaeva TE, Petrov VA, Sokolov VV (1981) Emissivity of stoichiometric zirconium and titanium carbides at high-temperatures. TVT 19(2):313–320Google Scholar
  33. 33.
    Fisenko AI, Lemberg V (2012) Radiative properties of stoichiometric hafnium, titanium, and zirconium carbides: thermodynamics of thermal radiation. Int J Thermophys 33(3):513–527CrossRefGoogle Scholar
  34. 34.
    Dewitt DP, Nutter GD (1988) Theory and practice of radiation thermometry. Willy, New YorkCrossRefGoogle Scholar
  35. 35.
    Krein MG, Nudelman AA (1977) The Markov moment problem and extremal problems. Translations of mathematical monographs, vol 50. American Mathematical Society, ProvidenceGoogle Scholar
  36. 36.
    Malomuzh NP, Fisenko AI (1983) Application limits of phenomenological theories of the dielectric and magnetic relaxations. Fizika Zidkogo Sostoyaniy 11:90–95 (in Russian) Google Scholar
  37. 37.
    Malomuzh NP (1983) Investigation of the applicability region for the hydrodynamic description of longitudinal modes in liquids and gases. Ukr Fiz J 28(12):1833–1838Google Scholar
  38. 38.
    Fisenko AI, Lemberg V (2016) Thermal radiative and thermodynamic properties of solid and liquid uranium and plutonium carbides in the visible–near-infrared range. J Mater Sci 51(17):8737–8746.  https://doi.org/10.1007/s10853-016-0138-7 CrossRefGoogle Scholar
  39. 39.
    Fisenko AI, Lemberg V (2013) Generalized Wien’s displacement law in determining the true temperature of ZrB2–SiC-based ultra-high temperature ceramic: thermodynamics of thermal radiation. Int J Thermophys 34:486–495CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ONCFEC Inc.St. CatharinesCanada

Personalised recommendations