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TECHNICAL PAPERS: Melting and Solidification

Heat Transfer Characteristics of Melting Ice Spheres Under Forced and Mixed Convection

[+] Author and Article Information
Y. L. Hao, Y.-X. Tao

Department of Mechanical Engineering, Florida International University, Miami, FL 33199

J. Heat Transfer 124(5), 891-903 (Sep 11, 2002) (13 pages) doi:10.1115/1.1494090 History: Received October 24, 2001; Revised April 16, 2002; Online September 11, 2002
Copyright © 2002 by ASME
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References

Tkachev, A. G., 1953, “Heat Exchange in Melting and Freezing of Ice,” in Problem of Heat Transfer During Change of Phase: A Collection of Articles, AEC-tr-3405, translated from Russian, State Power Press, pp. 169–178.
Merk,  H. J., 1953, “The Influence of Melting and Anomalous Expansion on the Thermal Convection in Laminar Boundary Layers,” Appl. Sci. Res., 4, pp. 435–452.
Schenk, I., and Schenkels, F. M., 1968, “Thermal Free Convection from an Ice Sphere in Water,” Appl. Sci. Res., pp. 465–476.
Vanier,  Cr. R., and Tien,  C., 1970, “Free Convection Melting of Ice Spheres,” AIChE J., 16, pp. 76–82.
Eskandari, V., 1981, “Forced Convection Heat Transfer from Ice Spheres in Flowing Water,” Master’s thesis, University of Toledo, Toledo, OH.
Eskandari, V., Jakubowski, G. S., and Keith, T. G., 1982, “Heat Transfer from Spherical Ice in Flowing Water,” Joint AIAA/ASME Fluids, Plasma, Thermophysics, and Heat Transfer Conference, St Louis, MO, ASME 82-HT-58, pp. 1–5.
Anselmo, A., Prasad, V., and Koziol, J., 1991, “Melting of a Sphere when Dropped in a Pool of Melt with Applications to Partially-Immersed Silicon Pellets,” Heat Transfer in Metals and Containerless Processing and Manufacturing, ASME HTD Vol. 162, pp. 75–82.
Anselmo,  A., Prasad,  V., Koziol,  J., and Gupta,  K. P., 1993, “Numerical and Experimental Study of a Solid-pellet Feed Continuous Czochralski Growth Process for Silicon Single Crystals,” J. Cryst. Growth, 131, pp. 247–264.
Mukherjee, M. K., Shih, J., and Prasad, V., 1994, “A Visualization Study of Melting of an Ice Sphere in a Pool of Water,” 1994 International mechanical Engineering Congress and Exposition, The Winter Annual Meeting, ASME 94-WA/HT-14, Chicago, Illinois, November 6–11, 1994.
Aziz, S. A., Janna, W. S., and Jakubowski, G. S., 1995, “Forced Convection Heat Transfer From an Isothermal Melting Ice Sphere Submerged in Flowing Water,” ASME HTD-Vol. 317-1, pp. 213–217.
McLeod,  P., Riley,  D. S., and Sparks,  R. S. J., 1996, “Melting of a Sphere in Hot Fluid,” J. Fluid Mech., 327, pp. 393–409.
Hao, Y. L., and Tao, Y. X., 1999, “Convective Melting of a Solid Particle in a Fluid,” Proceedings of the 3rd ASME/JSME Joint Fluids Engineering Conference, San Francisco, California, July 18–23, 1999, FEDSM99-7091, pp. 1–6.
Hao,  Y. L., and Tao,  Y. X., 2001, “Melting of Solid Sphere Under Forced and Mixed Convection: Flow Characteristics,” ASME J. Heat Transfer, 123, pp. 937–950.
Gebhart, B., 1993, Heat Conduction and Mass Diffusion, McGraw-Hill, Inc., New York, Chap. 4.
Kline,  S. L., and McClintock,  F. A., 1953, “Describing Uncertainties in Single-Sample Experiments,” Mech. Eng. (Am. Soc. Mech. Eng.), 75, pp. 3–8.

Figures

Grahic Jump Location
Temperature-time histories at the inlet and the ice center: Tl0=26°C,vl∞=0.06 m/s,Ts0=−16°C,d0=36 mm,Gr0/Re02=0.319. 1—inlet; 2—center of ice.
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Variations of total heat transfer rate, total latent heat for fusion, and total conducted heat into the inside with time in the melting process: Tl0=26°C,vl∞=0.06 m/s,Ts0=−16°C,d0=36 mm,Gr0/Re02=0.319. 1—convective heat transfer from water to interface; 2—total latent heat for fusion; 3—heat conducted into the inside of ice.
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Schematic of the test apparatus
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Volume element in the ice sphere and volume elements between t and t+dt
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Typical video pictures of the ice sphere in the melting process (water flows horizontally from the right side to the left side): (a) Side view; (b) top view.
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Shape change of ice particle in the melting process: Tl0=26°C,vl∞=0.06 m/s,Ts0=−16°C,d0=36 mm,Gr0/Re02=0.319. 1—0 s; 2—20 s; 3—35 s; 4—50 s; 5—65 s; 6—80 s; 7—95 s; 8—110 s; 9—125 s: (a) In Cartesian coordinates; (b) in spherical coordinates with the center of particle coinciding with the origin.
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Variation of Nusselt number as a function of (Gr/Re2) at different water temperatures: vl∞=0.06 m/s,Ts0=−8°C,d0=36 mm.
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Correlation and all of results for dimensionless average heat transfer coefficient in the present study: Tl0=4∼30°C,vl∞=0.01∼0.10 m/s,Ts0=−23∼0°C,d0=36 mm.
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Variation of diameters and shape factor with time in the melting process: Tl0=26°C,vl∞=0.06 m/s,Ts0=−16°C,d0=36 mm,Gr0/Re02=0.319. 1—diameter based on volume of ice, dV; 2—diameter based on surface area of ice, ds; 3—shape factor, ϕ.
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Local melting rate ṁ(θ) at different time in the melting process: Tl0=26°C,vl∞=0.06 m/s,Ts0=−16°C,d0=36 mm,Gr0/Re02=0.319.
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Local heat transfer coefficient h(θ) at different time in the melting process: Tl0=26°C,vl∞=0.06 m/s,Ts0=−16°C,d0=36 mm,Gr0/Re02=0.319.
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Local Nusselt number Nu(θ) at different time in the melting process: Tl0=26°C,vl∞=0.06 m/s,Ts0=−16°C,d0=36 mm,Gr0/Re02=0.319.
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Peak local Nusselt number Nupeak and the location θpeak during the melting process: 1—Tl0=26°C,vl∞=0.06 m/s,Ts0=−16°C,d0=36 mm,Gr0/Re02=0.319, 2—Tl0=16°C,vl∞=0.06 m/s,Ts0=−16°C,d0=36 mm,Gr0/Re02=0.093.
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Compared experimental results at different water velocities: –Tl0=16°C,vl∞=0.06 m/s,Ts0=−9°C,d0=36 mm,Gr0/Re02=0.093. - - - - - - Tl0=16°C,vl∞=0.04 m/s,Ts0=−9°C,d0=36 mm,Gr0/Re02=0.209. (a) R; (b) ṁ; (c) Nu.
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Compared experimental results at different water temperatures: –Tl0=30°C,vl∞=0.06 m/s,Ts0=−9°C,d0=36 mm,Gr0/Re02=0.440. - - - - - - Tl0=16°C,vl∞=0.06 m/s,Ts0=−9°C,d0=36 mm,Gr0/Re02=0.093. (a) R; (b) ṁ; (c) Nu.
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Experimental results at a slow water velocity: Tl0=21°C,vl∞=0.01 m/s,Ts0=−3°C,d0=36 mm,Gr0/Re02=6.98. (a) Shape change; (b) ṁ; (c) h; (d) Nu.
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Variation of melting rate of ice particle with time at different water velocities: Tl0=16°C,Ts0=−8°C,d0=36 mm.
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Variation of average heat transfer coefficient with time at different water velocities: Tl0=16°C,Ts0=−8°C,d0=36 mm.
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Variation of Nusselt number as a function of (Gr/Re2) at different water velocities: Tl0=16°C,Ts0=−8°C,d0=36 mm.
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Variation of melting rate of ice particle with time at different water temperatures: vl∞=0.06 m/s,Ts0=−8°C,d0=36 mm.
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Variation of average heat transfer coefficient with time at different water temperatures: vl∞=0.06 m/s,Ts0=−8°C,d0=36 mm.

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