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TECHNICAL PAPERS: Melting and Solidification

Melting of a Solid Sphere Under Forced and Mixed Convection: Flow Characteristics

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

Department of Mechanical Engineering, Tennessee State University, Nashville, TN 37209-1561

J. Heat Transfer 123(5), 937-950 (Mar 28, 2001) (14 pages) doi:10.1115/1.1389466 History: Received August 21, 2000; Revised March 28, 2001
Copyright © 2001 by ASME
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References

Tkachev, A. G., 1953, “Heat hExchange 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.
Schenk, J., and Schenkels, F. M., 1968, “Thermal Free Convection from an Ice Sphere in Water,” Appl. Sci. Res., pp. 465–476.
Vanier,  C. R., and Tien,  C., 1970, “Free Convection Melting of Ice Spheres,” AIChE J., 16, pp. 76–82.
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, 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,” ASME 94-WA/HT-14.
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.
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,” ASME 82-HT-58.
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,” Proc. ASME Heat Transfer Division, 1 ASME, New York, pp. 213–217.
Hao, Y. L., and Tao, Y. X., 1999, “Convective Melting of a Solid Particle in a Fluid,” Proc. 3rd ASME/JSME Joint Fluids Engineering Conference, P. A. Pfund et al., eds., ASME, New York.
Hao, Y. L., and Tao, Y. X., 1999, “Heat Transfer Characteristics in Convective Melting of a Solid Particle in a Fluid,” Proc. ASME Heat Transfer Division, 2 L. C. Witte, ed., ASME, New York, pp. 207–212.
Hao, Y. L., and Tao, Y. X., 2000, “Local Melting and Heat Transfer Characteristics in Convective Melting of a Solid Particle in a Fluid,” Proc. 2000 National Heat Transfer Conference, S. C. Yao et al., eds., ASME, New York.
Adrian,  R. J., 1986, “Multi-Point Optical Measurements of Simultaneous Vectors in Unsteady Flow—A Review,” Int. J. Heat Fluid Flow, 7, pp. 127–145.
Kline,  S. L., and McClintock,  F. A., 1953, “Describing Uncertainties in Single-Sample Experiments,” Mech. Eng. (Am. Soc. Mech. Eng.), 75, pp. 3–8.
Hassan,  Y. A., Schmidl,  W., and Ortiz-Villafuerte,  J., 1998, “Investigation of Three-Dimensional Two-Phase Flow Structure in a Bubbly Pipe Flow,” Meas. Sci. Technol., 9, pp. 1–18.
TSI, 1999, Instruction Manual of INSIGHT™ 2 & INSIGHT™ Stereo Particle Image Velocimetry Software (Version 2), TSI Incorporated, St. Paul; MN.
TSI, 1999, Reference Manual of the PIV System, TSI Incorporated, St. Paul, MN.

Figures

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Schematic of the test apparatus
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Test section and PIV system setup
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Typical instantaneous image of the measured flow field at t*=0.3:Vw=0.05 m/s,Tw=4°C,d0=36 mm,Ti,0=−15°C,ttotal=760 s.
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Flow field results in the axial plane: t*=0.0079,Vw=0.05 m/s,Tw=4°C,d0=36 mm,Ti,0=−15°C,Re0=1077,Gr0=883,Gr0/Re02=7.6 × 10−4,ttotal=760 s: (a) velocity vector distribution; (b) streamline; (c) z-component of rotation vector; (d) velocity component in x-direction; and (e) velocity component in y-direction.
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Flow field results in the axial plane: t*=0.3,Vw=0.05 m/s,Tw=4°C,d0=36 mm,Ti,0=−15°C,Re0=1077,Gr0=883,Gr0/Re02=7.6 × 10−4,ttotal=760 s: (a) velocity vector distribution; (b) streamline; and (c) z-component of rotation vector.
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Flow field results in the axial plane: t*=0.6,Vw=0.05 m/s,Tw=4°C,d0=36 mm,Ti,0=−15°C,Re0=1077,Gr0=883,Gr0/Re02=7.6 × 10−4,ttotal=760 s: (a) velocity vector distribution; (b) streamline; and (c) z-component of rotation vector.
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Flow field results in the axial plane: t*=0.9,Vw=0.05 m/s,Tw=4°C,d0=36 mm,Ti,0=−15°C,Re0=1077,Gr0=883,Gr0/Re02=7.6 × 10−4,ttotal=760 s: (a) velocity vector distribution; (b) streamline; and (c) z-component of rotation vector.
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Flow field results in the axial plane: t*=0.5,Vw=0.01 m/s,Tw=4°C,d0=36 mm,Ti,0=−20°C,Re0=215,Gr0=883,Gr0/Re02=0.019,ttotal=1614 s: (a) velocity vector distribution; (b) streamline; and (c) z-component of rotation vector.
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Flow field results in the axial plane: t*=0.5,Vw=0.05 m/s,Tw=4°C,d0=36 mm,Ti,0=−20°C,Re0=1077,Gr0=883,Gr0/Re02=7.6 × 10−4,ttotal=1009 s: (a) velocity vector distribution; (b) streamline; and (c) z-component of rotation vector.
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Flow field results in the axial plane: t*=0.5,Vw=0.10 m/s,Tw=4°C,d0=36 mm,Ti,0=−20°C,Re0=2154,Gr0=883,Gr0/Re02=1.9 × 10−4,ttotal=689 s: (a) velocity vector distribution; (b) streamline; and (c) z-component of rotation vector.
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Flow field results in the axial plane at a high water temperature: Vw=0.01 m/s,Tw=30°C,d0=36 mm,Ti,0=−20°C,Re0=316,Gr0=6.8 × 106,Gr0/Re02=68.1,t*=0.5,ttotal=229 s: (a) velocity vector distribution; (b) streamline; (c) z-component of rotation vector; (d) velocity component in x-direction; and (e) velocity component in y-direction.
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Flow field results in the axial plane at a high water temperature: Vw=0.05 m/s,Tw=30°C,d0=36 mm,Ti,0=−20°C,Re0=1579,Gr0=6.8 × 106,Gr0/Re02=2.73,t*=0.5,ttotal=133 s: (a) velocity vector distribution; (b) streamline; (c) z-component of rotation vector; (d) velocity component in x-direction; and (e) velocity component in y-direction.
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Video images of melting dyed ice sphere at different water velocities: Tw=4°C,d0=36 mm,Ti,0=−20°C,Gr0=883,t*=0.3: (a) Vw=0.01 m/s,Re0=215,Gr0/Re02=0.019,ttotal=1542 s; (b) Vw=0.05 m/s,Re0=1077,Gr0/Re02=7.6 × 10−4,ttotal=816 s; and (c) Vw=0.10 m/s,Re0=2154,Gr0/Re02=1.9× 10−4,ttotal=567 s
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Video images of melting, dyed ice sphere at different water velocities and a high water temperature: Tw=30°C,d0=36 mm,Ti,0=−20°C,Gr0=6.8 × 106,t*=0.3: (a) Vw=0.01 m/s,Re0=316,Gr0/Re02=68.1,ttotal=209 s; (b) Vw=0.05 m/s,Re0=1579,Gr0/Re02=2.73,ttotal=141 s; and (c) Vw=0.10 m/s,Re0=3158,Gr0/Re02=0.682,ttotal=82 s
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Variation of flow separation locations with time at different upstream velocities in melting processes: Tw=4°C,d0=36 mm,Ti,0=−20°C,Gr0=883: (a) upper separation points; and (b) lower separation points.
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Variation of flow separation locations with time at different upstream velocities in melting processes: Tw=30°C,d0=36 mm,Ti,0=−20°C,Gr0=6.8 × 106: (a) upper separation points; and (b) lower separation points.
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Flow field around a melting ice sphere in the axial plane: t*=0.0079,Vw=0.05 m/s,Tw=4°C,d0=36 mm,Ti,0=−15°C,Re0=1077,Gr0=883,Gr0/Re02=7.6 × 10−4,ttotal=760 s: (a) velocity vector distribution; (b) streamline; and (c) z-component of rotation vector.
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Flow field around a plastic sphere in the axial plane: Vw=0.05 m/s,Tw=4°C,d0=36 mm,Ti=4°C,Re0=1149,Gr0=0,Gr0/Re02=0: (a) velocity vector distribution; (b) streamline; and (c) z-component of rotation vector.
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Velocity components in x and y-direction along different x lines around a melting sphere: t*=0.0079,Vw=0.05 m/s,Tw=4°C,d0=36 mm,Ti,0=−15°C,Re0=1077,Gr0=883,Gr0/Re02=7.6 × 10−4,ttotal=760 s. (Broken lines indicate a projected result below the ice sphere where no PIV data are available.): (a) velocity component in x-direction; and (b) velocity component in y-direction.

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