Abstract
A model is presented for the prediction of the interfacial heat-transfer coefficient during the unidirectional solidification vertically upward of an Al-7 wt pct Si alloy cast onto a water cooled copper chill. It has been experimentally determined that the casting surfaces were convex toward the chill, probably due to the deformation of the initial solidified skin of the casting. The model was, therefore, based upon a determination of the (macroscopic) nominal contact area between the respective rough surfaces and, within this region, the actual (microscopic) contact between the casting and the chill surfaces. The model produced approximate agreement with both experimentally determined values of the heat-transfer coefficient and the measured curvature of the casting surface and showed a reasonable agreement with measured temperatures in the casting and the chill also. A common experimental technique for the experimental determination of the heat-transfer coeffcient involves the assumption of one-dimensional heat transfer only. An implication of the approach adopted in this model is that the heat transfer in the region of the casting-chill interface may be two-dimensional, and the subsequent error in the experimentally determined values is discussed.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. Ho and R.D. Pehlke: AFS Trans., 1984, vol. 92, pp. 587–98.
K. Ho and R.D. Pehlke: Metall. Trans. B, 1985, vol. 16B, pp. 585–94.
R.D. Pehlke: Proc. Modelling of Casting, Welding and Advanced Solidification Processes VII, M. Cross and J.J. Campbell, eds., TMS, Warrendale, PA, 1995, pp. 373–80.
Y. Nishida, W. Droste, and S. Engler: Metall. Trans. B, 1986, vol. 17B, pp. 833–44.
M. Trovant and S. Argyropolis: Proc. Computational Fluid Dynamics and Heat/Mass Transfer Modeling in the Metallurgical Industry, Montreal, Aug. 24–29, 1996, Canadian Institute of Mining, Montreal, Canada, 1996, pp. 108–22.
J. Isaac, G.P. Reddy, and G.K. Sharma: J. Inst. Eng.: Metall. Mater. Sci. (India), 1989, vol. 69, pp. 17–22.
H. Huang, J.L. Hill, V.K. Suri, and J.T. Berry: Proc. Modelling of Casting, Welding and Advanced Solidification Processes V, TMS, Warrendale, PA, 1991, pp. 65–70.
H. Huang, J.L. Hill, and J.T. Berry: Cast Met., 1993, vol. 5, pp. 212–16.
H.R. Shahverdi, F. Farhadi, A. Karimitaheri, P. Davami, and K. Asgari: Cast Met., 1994, vol. 6, pp. 231–36.
M. Bellet, F. Decultieux, M. Menai, F. Bay, C. Levaillant, J.-L. Chenot, P. Schmidt, and I.L. Svensson: Metall. Mater. Trans. B, 1996, vol. 27B, pp. 81–99.
O. Jaouen and M. Bellet: Proc. Modelling of Casting, Welding and Advanced Solidification Processes VIII, TMS, Warrendale, PA, 1998, pp. 739–46.
D.G.R. Sharma and M. Krishnan: AFS Trans., 1991, vol. 99, pp. 429–38.
P.M. Mathew, J.W. Devaal, and P.A. Krueger: Can. Met. Q., 1989, vol. 28, pp. 271–83.
F. Chiesa: AFS Trans., 1990, vol. 98, pp. 193–200.
I.L. Svensson and P. Schmidt: Cast Met., 1993, vol. 6, pp. 127–30.
W.D. Griffiths: Proc. 3rd Pacific Rim Int. Conf. Modelling of Casting and Solidification Processes, Beijing, Dec. 9–11, 1996, International Academic Publishers, Beijing, 1996, pp. 64–69.
W.D. Griffiths: Metall. Mater. Trans. B, 1999, vol. 30B, pp. 473–82.
R. Kayikci and W.D. Griffiths: Foundryman, 1999, vol. 92, pp. 267–73.
D. Shu-xin, E. Niyama, K. Anzai, and N. Matsumoto: Cast Met., 1993, vol. 6, pp. 115–20.
S.X. Dong, E. Niyama, and K. Anzai: Iron Steel Inst. Jpn. Int., 1995, vol. 35, pp. 730–36.
B.G. Thomas and J.T. Parkman: Proc. Solidification 1998, TMS, Warrendale, PA, 1998, pp. 509–20.
J.P. Holman: Heat Transfer, 6th ed., McGraw-Hill Book Company, New York, NY, 1986, pp. 131–206.
K. Ho and R.D. Pehlke: AFS Trans., 1983, vol. 91, pp. 689–98.
N.A. El-Mahallawy and A.M. Assar: J. Mater. Sci., 1991, vol. 26, pp. 1729–33.
Assessment of Surface Texture, Part 1. Methods and Instrumentation. BS 1134: Part 1: 1988, British Standards Institution, London, 1988.
E.H. Kennard: Kinetic Theory of Gases, McGraw-Hill Book Company, New York, NY, 1938, pp. 311–27.
M.M. Yovanovich, J.W. DeVaal, and A.H. Hegazy: Proc. AIAA/ASME 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conf., The American Institute of Aeronautics and Astronautics, New York, NY, 1982, pp. 1–7.
J.A. Greenwood: Trans. ASME, J. Lubr. Technol., 1967, vol. 89F, pp. 81–91.
J.A. Greenwood and J.P.B. Williamson: Proc. R. Soc. London, A, 1966, vol. 295, pp. 300–19.
B.B. Mikic: Int. J. Heat Mass Transfer, 1974, vol. 17, pp. 205–14.
Metals Handbook, 10th ed., ASM INTERNATIONAL, Materials Park, OH, 1990, vol. 2, pp. 164–65.
B. Forest and S. Bercovici: Proc. Solidification Technology in the Foundry and Cast House, Coventry, England, Sept. 15–17, 1980, The Metals Society, London, 1980, pp. 607–12.
B.M. Drapkin and V.K. Kononenko: Russ. Metall., 1993, vol. 6, pp. 74–77.
Rough Surfaces, T.R. Thomas, ed., Contact Mechanics, Longman, London, 1982, pp. 168–88.
D.J. Whitehouse: Handbook of Surface Metrology, IOP Publishing Ltd., Bristol, 1994, pp. 762–75.
D. Tabor: The Hardness of Metals, Oxford University Press, Oxford, United Kingdom, 1951.
M.G. Cooper, B.B. Mikic, and M.M. Yovanovich: Int. J. Heat Mass Transfer, 1969, vol. 12, pp. 279–99.
M.R. Sridhar and M.M. Yovanovich: J. Thermophys. Heat Transfer, 1994, vol. 8, pp. 633–40.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Griffiths, W.D. A model of the interfacial heat-transfer coefficient during unidirectional solidification of an aluminum alloy. Metall Mater Trans B 31, 285–295 (2000). https://doi.org/10.1007/s11663-000-0047-6
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11663-000-0047-6