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TECHNICAL PAPERS

Solidification of a Finite Medium Subject to a Periodic Variation of Boundary Temperature

[+] Author and Article Information
Z. Dursunkaya

Mechanical Engineering Department, Middle East Technical University, Inonu Bulvari, Ankara 06531, Turkey

S. Nair

Mechanical, Materials and Aerospace Engineering Department, Illinois Institute of Technology, Engineering 1 Building, 10 West 32nd Street, Chicago, IL 60616-3793

J. Appl. Mech 70(5), 633-637 (Oct 10, 2003) (5 pages) doi:10.1115/1.1604836 History: Received July 04, 2002; Revised February 05, 2003; Online October 10, 2003
Copyright © 2003 by ASME
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References

Carslaw, H. S., and Jaeger, J. C., 1954, Conduction of Heat in Solids, Oxford University Press, Oxford, UK.
Tao,  L. N., 1978, “The Stefan Problem With Arbitrary Initial and Boundary Conditions,” Q. Appl. Math., 36, pp. 223–233.
Tao,  L. N., 1981, “The Exact Solutions of Some Stefan Problems With Prescribed Heat Flux,” ASME J. Appl. Mech., 48, pp. 732–736.
Crank, J., 1988, Free and Moving Boundary Problems, Oxford University Press, Oxford, UK.
Rubinstein, L. I., 1971, The Stefan Problem, American Mathematical Society, Providence, RI (English translation).
Ockendon, J. R., and Hogkins, W. R., 1975, Moving Boundary Problems in Heat Flow and Diffusion, Clarendon Press, Oxford, UK.
Wilson, D. G., Solomon, A. D., and Boggs, P. T., 1978, Moving Boundary Problems, Academic Press, San Diego, CA.
Fukusako, S., and Seki, N., 1987, “Fundamental Aspects of Analytical and Numerical Methods on Freezing and Melting Heat-Transfer Problems,” Annual Review of Numerical Fluid Mechanics and Heat Transfer, T. C. Chawla, ed., Hemisphere, Washington, DC, 1 , pp. 351–402.
Weinbaum,  S., and Jiji,  L. M., 1977, “Singular Perturbation Theory for Melting and Freezing in Finite Domains Initially not at the Fusion Temperature,” ASME J. Appl. Mech., 44, pp. 25–30.
Charach,  Ch., and Zoglin,  P., 1985, “Solidification in a Finite, Initially Overheated Slab,” Int. J. Heat Mass Transfer, 28, pp. 2261–2268.
Nair, S., 1994, “Numerical Solution of Moving Boundary Problems Using Integral Equations,” ASME AMD 182, Transport Phenomena in Solidification, ASME, New York, AMD-182, pp. 109–118.
Rizwan-uddin  , 1999, “One-Dimensional Phase Change With Periodic Boundary Conditions,” Numer. Heat Transfer, Part A, 35, pp. 361–372.
Dursunkaya,  Z., and Nair,  S., 1990, “A Moving Boundary Problem in a Finite Domain,” ASME J. Appl. Mech., 57, pp. 50–56.

Figures

Grahic Jump Location
Solidification domain and temperatures
Grahic Jump Location
Time for complete solidification in a finite slab
Grahic Jump Location
Interface motion and boundary temperature variation for St1=0.1 and γ=0.25
Grahic Jump Location
Interface motion and boundary temperature variation for St1=1 and γ=0.25
Grahic Jump Location
Interface motion and boundary temperature variation for St1=0.1 and γ=0.5
Grahic Jump Location
Interface motion and boundary temperature variation for St1=0.1 and γ=0.5 for small time
Grahic Jump Location
Interface motion and boundary temperature variation for St1=0.5 and γ=0.5
Grahic Jump Location
Temperature distribution during solidification for St1=0.5,St2=0.5, and γ=0.5

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