Advertisement

Radiation–Conduction Heat-Transfer Study for Mold Flux by Thermoviewer-Enhanced Infrared Emitter Technique

  • Wanlin Wang
  • Kaixuan Zhang
  • Haihui ZhangEmail author
Article
  • 8 Downloads

Abstract

A thermoviewer-enhanced infrared emitter technique was developed in this article to study the heat-transfer behavior of mold flux in the continuous casting mold. Then, a radiation–conduction heat-transfer model was built to determine the radiative/conductive heat flux, thermal conductivity, and optical properties of slag. The results showed that the mold/slag interfacial thermal resistance decreases with the increasing temperature of slag surface at the mold side, and then reaches the minimum when the slag surface is the hottest, and finally increases slightly with further increase in slag crystallization. In addition, the radiative heat flux decreases with the increasing depth of radiation propagating into the slag. While the amount of heat of radiation lost is being converted to produce an additional radiative heat source to heat the slag, the increase in the conductive heat flux in the slag is realized. Furthermore, the apparent transmittivity is obtained as 0.63 for the glassy slag disk and as 0.41 for the partially crystallized slag disk. Besides, when mold heat flux decreases from the maximum to a saturation value due to the further slag crystallization, the corresponding apparent transmittivity of slag disk decreases from 0.58 to 0.41, and the ratio of the heat across the slag disk by radiation decreases from 67.3 to 50.0 pct.

Nomenclature

C

Specific heat (J/kg·K)

C0

Stefan–Boltzmann constant, 5.670 × 10−8 W/m2 K4

D

Thickness of slag disk (m)

En(x)

Exponential integral function

G(τ)

Incident radiation (W·m−2)

hf

Convective heat-transfer coefficient (W/m2 K)

I

Intensity of radiation (W/m2sr)

Ib

Blackbody intensity (Planck function) (W/m2sr)

l

Free path of phonons (m)

Mea

Total number of measurement (–)

Mt

Point of maximum temperature in the slag (mm)

n1

Refractive index of slag bottom surface (–)

n2

Refractive index of slag top surface (–)

q

Heat flux (W m−2)

qb

Bare copper heat flux (W m−2)

qc

Conductive flux in the slag (W m−2)

qlamp

Radiative flux of infrared lamp (W m−2)

qm

Mold heat flux (W m−2)

Qr

Radiative flux in the slag (W m−2)

Rint

Thermal resistance between mold and slag (m2 K W−1)

s

Geometric path length (m)

\( \hat{s} \)

Unit vector into a given direction (–)

T

Temperature (K))

T1

Temperature of slag bottom surface (K)

T2

Slag top surface temperature (K)

Tf

Temperature of ambient air (K)

Tm

Temperature of mold surface (K)

V

Sonic velocity (m/s)

x, y, z

Cartesian coordinates (m)

Greek Symbols

β

Extinction coefficient (m−1)

βj

Extinction coefficient of j-th medium (m−1)

ε1

Emissivity of mold–slag interface (–)

ε2

Emissivity of air–crystal interface (–)

εm

Emissivity of mold surface (–)

θ

Angle between the direction of the radiation intensity and the positive vertical direction (rad)

λ

Thermal conductivity (W/m K)

λr

Radiation conductivity (W/m K)

κ

Absorption coefficient (m−1)

κj

Absorption coefficient of j-th medium (m−1)

μ

Direction cosine (of polar angle), cosθ (–)

ρ

Density (kg/m3)

ρ1

Reflectivity of mold–slag interface (–)

ρ2

Reflectivity of air–crystal interface (–)

ρm

Reflectivity of mold surface (–)

σs

Scattering coefficient (m−1)

σs ,j

Scattering coefficient of j-th medium (m−1)

τ(z)

Optical depth τ(z) =  \(\int\nolimits_{0}^{z} \beta dz\)(–)

τs

Slag optical thickness (–)

ω

Single scattering albedo (–)

ωj

Single scattering albedo of j-th medium (–)

ψ

Azimuthal angle (rad)

Ω

Solid angle (sr)

Subscripts

c

Conduction

j

Glass (g), crystal (c)

m

Copper mold

f

Atmosphere

r

Radiation

Notes

Acknowledgments

The financial supports from the National Natural Science Foundation of China (51661130154, 51704333, and U1760202), Newton Advanced Fellowship (NA150320), and the Fundamental Research Funds for the Central Universities of Central South University (2018zzts437) are gratefully acknowledged.

References

  1. 1.
    M. Hanao, M. Kawamoto, and A. Yamanaka: ISIJ Int., 2012, vol. 52, pp. 1310–19.CrossRefGoogle Scholar
  2. 2.
    A.W. Cramb: ISIJ Int., 2014, vol. 54, pp. 2665–71.CrossRefGoogle Scholar
  3. 3.
    M. Ozawa, M. Susa, T. Goto, R. Endo, and K.C. Mills: ISIJ Int., 2006, vol. 46, pp. 413–19.CrossRefGoogle Scholar
  4. 4.
    M. Kawamoto, Y. Tsukaguchi, N. Nishida, T. Kanazawa, and S. Hiraki: ISIJ Int., 1997, vol. 37, pp. 134–39.CrossRefGoogle Scholar
  5. 5.
    M. Susa, A. Kushimoto, R. Endo, and Y. Kobayashi: ISIJ Int., 2011, vol. 51, pp. 1587–96.CrossRefGoogle Scholar
  6. 6.
    H. Nakada, M. Susa, Y. Seko, M. Hayashi, and K. Nagata: ISIJ Int., 2008, vol. 48, pp. 446–53.CrossRefGoogle Scholar
  7. 7.
    A. Yamauchi, K. Sorimachi, T. Sakuraya, and T. Fujii: ISIJ Int., 1993, vol. 33, pp. 140–47.CrossRefGoogle Scholar
  8. 8.
    H. Shibata, K. Kondo, M. Suzuki, and T. Emi: ISIJ Int., 1996, vol. 36, pp. S179–S182.CrossRefGoogle Scholar
  9. 9.
    J.W. Cho, T. Emi, H. Shibata, and M. Suzuki: ISIJ Int., 1998, vol. 38, pp. 834–42.CrossRefGoogle Scholar
  10. 10.
    K. Watanabe, M. Suzuki, K. Murakami, H. Kondo, A. Miyamoto, and T. Shiomi: Tetsu-to-Hagané, 1997, vol. 83, pp. 115-20.CrossRefGoogle Scholar
  11. 11.
    K. Nishioka, T. Maeda, and M. Shimizu: ISIJ Int., 2006, vol. 46, pp. 427–33.CrossRefGoogle Scholar
  12. 12.
    J.M. González de la C, T.M. Flores F, and A.H. Castillejos E: Metall. Mater. Trans. B, 2016, vol. 47, pp. 2509–23Google Scholar
  13. 13.
    J.W. Cho, H. Shibata, T. Emi, and M. Suzuki: ISIJ Int., 1998, vol. 38, pp. 440–46.CrossRefGoogle Scholar
  14. 14.
    S. Takahashi, R. Endo, T. Watanabe, M. Hayashi, and M. Susa: ISIJ Int., 2018, vol. 58, pp. 905–14.CrossRefGoogle Scholar
  15. 15.
    H.G. Ryu, Z.T. Zhang, J.W. Cho, G.H. Wen, and S. Sridhar: ISIJ Int., 2010, vol. 50, pp. 1142–50.CrossRefGoogle Scholar
  16. 16.
    C. Yang, G. Wen, X. Zhu, and P. Tang: J Non-cryst Solids, 2017, vol. 464, pp. 56–72.CrossRefGoogle Scholar
  17. 17.
    G. Wen, P. Tang. B. Yang, and X. Zhu: ISIJ Int., 2012, vol. 52, pp. 1179–85.CrossRefGoogle Scholar
  18. 18.
    C. Yang, G. Wen, Q. Sun, and P. Tang: Metall. Mater. Trans. B, 2017, vol. 48, pp. 1292–307.CrossRefGoogle Scholar
  19. 19.
    G. Wen, S. Sridhar, P. Tang, X. Qi, and Y. Liu: ISIJ Int., 2007, vol. 47: pp. 1117–25.CrossRefGoogle Scholar
  20. 20.
    X. Long, S. He, Q. Wang, and P.C. Pistorius: Metall. Mater. Trans. B, 2017, vol. 48, pp. 1652–58.CrossRefGoogle Scholar
  21. 21.
    K.L.S. Assis and P.C. Pistorius: Ironmak Steelmak, 2018, vol. 45, pp. 502-8.CrossRefGoogle Scholar
  22. 22.
    C. Yang, G. Wen, Q. Sun, and P. Tang: Int J Heat Mass Tran, 2017, vol. 110, pp. 523–38.CrossRefGoogle Scholar
  23. 23.
    J.Y. Park and I. Sohn: Int J Heat Mass Tran, 2017, vol. 109, pp. 1014–25.CrossRefGoogle Scholar
  24. 24.
    W. Wang, Zhou. L, and K. Gu: ., 2010, vol. 16, pp. 913–20CrossRefGoogle Scholar
  25. 25.
    W. Wang and A.W. Cramb: Steel Res Int, 2008, vol. 79, pp. 271–77.CrossRefGoogle Scholar
  26. 26.
    M. Susa, A. Kushimoto, H. Toyota, M. Hayashi, R. Endo, and Y. Kobayashi: ISIJ Int., 2009, vol. 49, pp. 1722–29.CrossRefGoogle Scholar
  27. 27.
    D.W. Yoon, J.W. Cho, and S.H. Kim: Metall. Mater. Trans. B, 2017, vol. 48, pp. 1951–61.CrossRefGoogle Scholar
  28. 28.
    D.W. Yoon, J.W. Cho, and S.H. Kim: Met Mater Int, 2015, vol. 21, pp. 580–87.CrossRefGoogle Scholar
  29. 29.
    J.W. Cho, H. Shibata, T. Emi, and M. Suzuki: ISIJ Int., 1998, vol. 38, pp. 268–75.CrossRefGoogle Scholar
  30. 30.
    J. Diao, B. Xie, N. Wang, S. He, Y. Li, and F. Qi: ISIJ Int., 2007, vol. 47, pp. 1294–99.CrossRefGoogle Scholar
  31. 31.
    J. Diao, B. Xie, and J. Xiao: Ironmak Steelmak, 2009, vol. 36, pp. 610–14.CrossRefGoogle Scholar
  32. 32.
    W. Wang, X. Long, H. Zhang and P. Lyu: ISIJ Int., 2018, vol. 58, pp. 1695–704.CrossRefGoogle Scholar
  33. 33.
    H. Zhang and W. Wang: Metall. Mater. Trans. B, 2017, vol. 48, pp. 779–93.CrossRefGoogle Scholar
  34. 34.
    J.Y. Park, E.Y. Ko, J. Choi, and I. Sohn: Met. Mater. Int., 2014, vol. 20, pp. 1103–14.CrossRefGoogle Scholar
  35. 35.
    E.Y. Ko, J. Choi, J.Y. Park, and I. Sohn: Met. Mater. Int., 2014, vol. 20, pp. 141–51.CrossRefGoogle Scholar
  36. 36.
    H. Zhang, W. Wang, F. Ma, and L. Zhou: Metall. Mater. Trans. B, 2015, vol. 46, pp. 2361–73.CrossRefGoogle Scholar
  37. 37.
    H. Zhang and W. Wang: Metall. Mater. Trans. B, 2016, vol. 47, pp. 920–31.CrossRefGoogle Scholar
  38. 38.
    K.C. Mills, L. Courtney, R.F. Brooks, and B.J. Monaghan: ISIJ Int., 2000, vol. 40, pp. S120–S129.CrossRefGoogle Scholar
  39. 39.
    Y. Kang, J. Lee, and K. Morita: ISIJ Int., 2014, vol. 54, pp. 2008–16CrossRefGoogle Scholar
  40. 40.
    C Bardos, F Golse, and B Perthame: Commun Pur Appl Math, 1987, vol. 40, 691-721.CrossRefGoogle Scholar
  41. 41.
    K.C. Mills and M. Guo: ISIJ Int., 2014, vol. 54, pp. 2000–7.CrossRefGoogle Scholar
  42. 42.
    S.P. Andersson and C. Eggertson: Ironmak Steelmak, 2015, vol. 42, pp. 456–64.CrossRefGoogle Scholar
  43. 43.
    K. Gu, W. Wang, L. Zhou, F. Ma, and D. Huang: Metall. Mater. Trans. B, 2012, vol. 43, pp. 937–45.CrossRefGoogle Scholar
  44. 44.
    K. Gu, W. Wang, J. Wei, H. Matsuura, F. Tsukihashi, I. Sohn, and D.J. Min: Metall. Mater. Trans. B, 2012, vol. 43, pp. 1393–404.CrossRefGoogle Scholar
  45. 45.
    W. Wang, K. Gu, L. Zhou, F. Ma, I. Sohn, D.J. Min, H. Matsuura, and F. Tsukihashi: ISIJ Int., 2011, vol. 51, pp. 1838–45.CrossRefGoogle Scholar
  46. 46.
    W. Wang and A.W. Cramb: ISIJ Int, 2005, vol. 45, pp. 1864–70.CrossRefGoogle Scholar
  47. 47.
    M.F. Modest: Radiation heat transfer, 3rd Ed, Academic press, Cambridge, MA, 2013, pp. 480–94.CrossRefGoogle Scholar
  48. 48.
    J. V. Beck, B. Blackwell, and C.R. StClair. Jr: Inverse heat conductionIII-Posed Problems. Wiley, New York, 1985, pp. 267–79.Google Scholar
  49. 49.
    H. Ohta, H. Shibata, T. Emi, and Y Waseda: J Jpn I Met, 1997, vol. 61, pp. 350–7.CrossRefGoogle Scholar
  50. 50.
    M.N. Özisik: Heat conduction, 2nd ed, John Wiley & Sons, New York, NY, 1993, pp. 372-91.Google Scholar
  51. 51.
    Y.A. Cengel, M.N. Özisik, and Y. Yener: J Heat Trans-T ASME, 1984, vol. 106, pp. 248–52.CrossRefGoogle Scholar
  52. 52.
    Y. A. Cengel, M. N. Özisik, and Y. Yener: Int J Heat Mass Tran, 1984, vol. 27, pp. 1919–22.CrossRefGoogle Scholar
  53. 53.
    Y.A. Cengel, and M.N. Özisik: J Quant Spectrosc Ra, 1985, vol. 34, pp. 263–70.CrossRefGoogle Scholar
  54. 54.
    M.N. Özisik and H.R.B. Orlande: Inverse heat transfer: fundamentals and applications. 1st ed, Taylor and Francis, New York, 2000, pp. 35–114.Google Scholar
  55. 55.
    M. Susa, K.C. Mills, M.J. Richardson, R. Taylor, and D. Stewart: Ironmaking & steelmaking, 1994, vol. 21, pp. 279-86.Google Scholar
  56. 56.
    K. Nagata, M. Susa, and K. S. Goto: Tetsu-to-Hagané, 1983, vol. 69, pp. 1417-24.CrossRefGoogle Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  1. 1.School of Metallurgy and EnvironmentCentral South UniversityChangshaChina

Personalised recommendations