Advertisement

Metallurgical and Materials Transactions B

, Volume 6, Issue 1, pp 131–142 | Cite as

The solidification of pure metals (and eutectics) under uni-directional heat flow conditions: II. Solidification in the presence of superheat

  • A. W. D. Hills
  • S. L. Malhotra
  • M. R. Moore
Solidification

Abstract

The generalized integral-profile method previously developed2 to predict the solidification rates of pure metals and eutectic alloys under a range of cooling conditions has been extended to treat solidification rates in the presence of super heat. Heat transfer within the liquid metal has been characterized in terms of a single parameter for which a heat balance on the liquid yields an ordinary nonlinear equation. This equation is additional to the two equations derived previously for the growth of the solid metal, and the three equations have been solved simultaneously using a Runge-Kutta technique. Solutions have been obtained for heat transfer conditions that can be reproduced accurately in laboratory experiments. The results of a series of such experiments are also presented and shown to agree very well with the theoretical predictions.

In carrying out the analysis, it has been shown that a number of different cooling and solidification modes can occur during the solidification of superheated liquid metal, the solidification process following one of two possible routes through these modes. This presents a useful approach to the analysis of this solidification problem and, indeed, of more complicated problems since the logic of the computer program used in the analysis is closely related to the logic of the solidification process.

Keywords

Heat Transfer Heat Flux Metallurgical Transaction Liquid Metal Solidification Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. R. Goodman:Trans. ASM, 1958, vol. 80, p. 335.Google Scholar
  2. 2.
    A. W. D. Hills:Trans. TMS-AIME, 1969, vol. 245, p. 1471.Google Scholar
  3. 3.
    R. H. Tien and G. E. Geiger:J. Heat Transfer, 1967, vol. 89, p. 230.Google Scholar
  4. 4.
    R. G. Tien and G. E. Geiger:J. Heat Transfer, 1968, vol. 90, p. 27.Google Scholar
  5. 5.
    V. Kroump, R. H. Tien, and T. F. Perzak:Trans. TMS-AIME, 1968, vol. 242, p. 1283.Google Scholar
  6. 6.
    T. R. Goodman and J. J. Shea:J. Appl. Mech., 1960, vol. 27, p. 16.Google Scholar
  7. 7.
    A. W. D. Hills and M. R. Moore:Trans. TMS-AIME, 1969, vol. 245, p. 1481.Google Scholar
  8. 8.
    J. K. Brimacombe and F. Weinberg:JISI, 1973, vol. 211, p. 24.Google Scholar
  9. 9.
    V. S. Aparci:Conduction Heat Transfer, p. 94, Addison-Wesley, New York, 1966.Google Scholar
  10. 10.
    M. R. Moore: Ph.D. Thesis, London University, 1966.Google Scholar
  11. 11.
    S. Malhotra: Ph.D. Thesis, London University, 1969.Google Scholar
  12. 12.
    R. W. Ruddle:The Solidification of Castings, Inst. of Metals, London. Monograph and Report Series, No. 7, 1957.Google Scholar
  13. 13.
    C. J. Smithels:Metals Reference Book, 3rd Edition, Butterworths (London), 1962.Google Scholar
  14. 14.
    M. Hansen:Constitution of Binary Alloys, 2nd Edition, McGraw-Hill, New York, 1958.Google Scholar
  15. 15.
    H. S. Carslaw and J. C. Jaeger:Conduction of Heat in Solids, p. 285, Oxford University Press, London, 1959.Google Scholar
  16. 16.
    R. W. Ruddle and A. L. Mincher:J. Inst. Metal, 1950, vol. 77, p. 1.Google Scholar
  17. 17.
    C. W. Briggs and R. A. Gezellius:Trans. Amer. Foundryman's Ass., 1947, vol. 55, p. 62.Google Scholar
  18. 18.
    E. Spinat: Ph.D. Thesis, London University, 1971.Google Scholar
  19. 19.
    C. M. Read: B.Sc. Project Thesis, Sheffield Polytechnic, 1972.Google Scholar
  20. 20.
    A. W. D. Hills and M. R. Moore:Chemical Metallurgy of Iron and Steel, p. 221, ISI, 1973.Google Scholar

Copyright information

© The Minerals, Metals & Materials Society - ASM International - The Materials Information Society 1975

Authors and Affiliations

  • A. W. D. Hills
    • 1
  • S. L. Malhotra
    • 2
  • M. R. Moore
    • 3
  1. 1.Metallurgy DepartmentSheffield PolytechnicSheffieldsEngland
  2. 2.Banares Hindu UniversityVaranasi-5India
  3. 3.United States Steel CorporationMonroeville

Personalised recommendations