A comparison of hyperbolic and parabolic models of phase change of a pure metal

International Journal of Heat and Mass Transfer

Volumn 52, Issue 5-6, 2009, Pages 1177-1184

  Liu, Haibo ^a   Bussmann, Markus ^a   Mostaghimi, Javad ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Hyperbolic; Interface tracking; Non equilibrium; Rapid solidification; Relaxation time; Undercooling

Indexed keywords

CRYSTALLIZATION; DYNAMICS; HEAT CONDUCTION; HEAT EXCHANGERS; HEAT TRANSFER; PHASE INTERFACES; RELAXATION PROCESSES; SOLIDIFICATION; THERMOANALYSIS; THERMODYNAMICS; UNDERCOOLING;

EQUILIBRIUM EFFECTS; EQUILIBRIUM TEMPERATURES; EXTENDED IRREVERSIBLE THERMODYNAMICS; FOURIER; FUNCTION OF TIMES; HYPERBOLIC; HYPERBOLIC EQUATIONS; HYPERBOLIC HEAT CONDUCTION EQUATIONS; INTERFACE TRACKING; INTERFACE VELOCITIES; NON-EQUILIBRIUM; PARABOLIC MODELS; PHASE CHANGES; PURE METALS; SECOND LAW OF THERMODYNAMICS; SOLIDIFICATION PROCESSES; SPRAY PARTICLES;

RAPID SOLIDIFICATION;

EID: 58149374407     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2008.08.030     Document Type: Article

References (30)

1. Wang G.-X., Goswami R., Sampath S., and Prasad V. Understanding the heat transfer and solidification of plasma-sprayed yttria-partially stabilized zirconia coatings. Mater. Manufacturing Process. 19 (2004) 259-272
2. Chae Y.K., Mostaghimi J., and Yoshida T. Deformation and solidification process of a super-cooled droplet impacting on the substrate under plasma spraying conditions. J. Sci. Technol. Adv. Mater. 1 (2000) 147-156
3. Pasandideh-Fard M., Chandra S., and Mostaghimi J. A three-dimensional model of droplet impact and solidification. Int. J. Heat Mass Transfer 45 (2002) 2229-2242
4. Wang G.-X., and Matthys E.F. Modeling of nonequilibrium surface melting and resolidification for pure metals and binary alloys. J. Heat Transfer 118 (1996) 944-951
5. Glass D.E. Formulation and solution of hyperbolic Stefan problem. J. Appl. Phys. 70 (1991) 1190-1197
6. Cattaneo C. Sulla conduzione del calore. Atti Sem. Mat. Fis. Univ. Modena 3 (1948) 83-101
7. Zanchini E. Hyperbolic-heat-conduction theories and nondecreasing entropy. Phys. Rev. B 60 (1999) 991-997
8. Coleman B.D., Fabrizio M., and Owen D.R. On the thermodynamics of second sound in dielectric crystals. Arch. Rational Mech. Anal. 80 (1982) 135-158
9. Mullis A.M. Rapid solidification within the framework of a hyperbolic conduction model. Int. J. Heat Mass Transfer 40 (1997) 4085-4094
10. Sobolev S.L. Rapid solidification under local nonequilibrium conditions. Phys. Rev. 55 (1997) 6845-6854
11. Galenko P.K., and Danilov D.A. Local nonequilibrium effect on rapid dendritic growth in a binary alloy melt. Phys. Lett. A 235 (1997) 271-280
12. Kurz W., and Fisher D.J. Fundamentals of Solidification. third ed. (1992), Trans Tech Publications pp. 22
13. Galenko P.K., and Danilov D.A. Model for free dendritic alloy growth under interfacial and bulk phase nonequilibrium conditions. J. Cryst. Growth 197 (1999) 992-1002
14. Ho J.-R., Kuo C.-P., and Jiaung W.-S. Study of heat transfer in multilayered structure within the framework of dual-phase-lag heat conduction model using lattice Boltzmann method. Int. J. Heat Mass Transfer 46 (2003) 55-69
15. Baumeister K.J., and Hamill T.D. Hyperbolic heat conduction equation - a solution for the semi-infinite body problem. J. Heat Transfer 91 (1969) 543-548
16. Barletta A., and Zanchini E. Hyperbolic heat conduction and local equilibrium: a second law analysis. Int. J. Heat Mass Transfer 40 (1997) 1007-1016
17. Bai C., and Lavine A.S. On hyperbolic heat conduction and the second law of thermodynamics. J. Heat Transfer 117 (1995) 256-263
18. Cahn J.W., Hillig W.B., and Sears G.W. The molecular mechanism of solidification. Acta Metallurgica 12 (1964) 1421-1439
19. Wang G.-X., and Matthys E.F. Mathematical simulation of melt flow, heat transfer and non-equilibrium solidification. Model. Simulation Mater. Sci. Eng. 10 (2002) 35-55
20. Turnbull D. Principles of Solidification, Thermodynamics in Physical Metallurgy (1950), American Society for Metals 282-306
21. Clyne T.W. Numerical treatment of rapid solidification. Metall. Mater. Trans. 15B (1984) 369-381
22. Levi C.G., and Mehrabian R. Heat flow during rapid solidification of undercooled metal droplets. Metall. Trans. 13A (1982) 221-234
23. J.P. Brazel, E.J. Nolan, Non-Fourier effects in the transmission of heat, in: Proceedings of the Sixth Conference on Thermal Conductivity, Dayton, Ohio, 1967.
24. Ueda R., and Mullin J.B. Crystal Growth and Characterization (1975), North-Holland 21-32
25. Tsao J.Y., Aziz M.J., Thompson M.O., and Peercy P.S. Asymmetric melting and freezing kinetics in silicon. Phys. Rev. Lett. 56 (1986) 2712-2715
26. Solomon A.D., Alexiades V., Wilson D.G., and Drake J.B. On the formulation of hyperbolic Stefan problems. Quart. Appl. Math. 43 (1985) 295-304
27. Patankar S.V. Numerical Heat Transfer and Fluid Flow (1980), Hemisphere pp. 32-60
28. Wang G.-X., Prasad V., and Matthys E.F. An interface-tracking numerical method for rapid planar solidification of binary alloys with application to microsegregation. Mater. Sci. Eng. A225 (1997) 47-58
29. Anderson D.A., Tannehill J.C., and Pletcher R.H. Computational Fluid Mechanics and Heat Transfer (1984), Hemisphere
30. G.-X. Wang, Experimental and numerical study of heat transfer and solidification for molten metal in contact with a cold substrate, PhD thesis, University of California, Santa Barbara, 1995.