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TECHNICAL PAPERS: Melting and Solidification

An Improved Quasi-Steady Analysis for Solving Freezing Problems in a Plate, a Cylinder and a Sphere

[+] Author and Article Information
Sui Lin

Department of Mechanical and Industrial Engineering, Concordia University, 1455 de Maisonneuve Blvd. W., Montreal, Quebec, Canada H3G 1M8

Zheng Jiang

Flomerics Inc., 257 Turnpike Road, Southborough, MA 01772, USA

J. Heat Transfer 125(6), 1123-1128 (Nov 19, 2003) (6 pages) doi:10.1115/1.1622719 History: Received February 04, 2003; Revised August 26, 2003; Online November 19, 2003
Copyright © 2003 by ASME
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References

Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, Oxford University Press, London, Chap. XI.
Lunardini, V. J., 1981, Heat Transfer in Cold Climates, Van Nostrand Reinhold Co., New York, Chap. 8.
London,  A. L., and Seban,  R. A., 1943, “Rate of Ice Formation,” Trans. ASME, 65, pp. 771–778.
Mennig,  J., and Ozisik,  M. N., 1985, “Coupled Integral Approach for Solving Melting or Solidification,” Int. J. Heat Mass Transfer, 28, pp. 1481–1485.
Caldwell,  J., and Kwan,  Y. Y., 2003, “On the Perturbation Method for the Stefan Problem With Time-Dependent Boundary Conditions,” Int. J. Heat Mass Transfer, 46, pp. 1497–1501.
Riley,  D. S., Smith,  F. I., and Poots,  G., 1974, “The Inward Solidification of Spheres and Circular Cylinders,” Int. J. Heat Mass Transfer, 17, pp. 1507–1516.
Poots,  G., 1962, “On the Application of Integral Methods to the Solution of Problems Involving the Solidification of Liquid Initially at Fusion Temperature,” Int. J. Heat Mass Transfer, 5, pp. 525–531.
Beckett, P. M., 1971, Ph.D. thesis, Hull University, England.
Allen,  D. N. de G., and Severn,  R. T., 1962, “The Application of the Relaxation Method to the Solution of Non-Elliptic Partial Differential Equations,” Q. J. Mech. Appl. Math., 15, p. 53.
Tao,  L. C., 1967, “Generalized Numerical Solutions of Freezing a Saturated Liquid in Cylinders and Spheres,” AIChE J., 13(1), p. 165.
Pedroso,  R. I., and Domoto,  G. A., 1973, “Perturbation Solutions for Spherical Solidification of Saturated Liquids,” ASME J. Heat Transfer, 95(1), pp. 42–46.

Figures

Grahic Jump Location
Relative errors, εst (quasi-steady solution) and εm (improved quasi-steady analysis) as functions of Stefan number, ST: (a) for cylindrical case: n=1; and (b) for spherical case: n=2.
Grahic Jump Location
Schematic diagram of freezing process in plate and cylinder/sphere coordinates
Grahic Jump Location
Dimensionless temperature distributions, T/T0 (exact solution), Tst/T0 (quasi-steady approximation) and Tm/T0 (improved quasi-steady analysis) with Ts/T0=1.5 and p=1.0
Grahic Jump Location
Proportionality constants, p (exact solution), pst (quasi-steady solution) and pm (improved quasi-steady analysis) as functions of c/L(Ts−T0) for freezing process in a plate
Grahic Jump Location
Relative errors, εst (quasi-steady solution) and εm (improved quasi-steady analysis) as a functions of c/L(Ts−T0) for freezing process in a plate

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