A numerical method for the Rubinstein binary-alloy problem in the presence of an under-cooled liquid

International Journal of Heat and Mass Transfer

Volumn 51, Issue 3-4, 2008, Pages 696-706

  Voller, V R ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Analytical solution; Binary alloy; Constitutional under cooling; Enthalpy method

Indexed keywords

ENTHALPY; HEAT TRANSFER; MASS TRANSFER; NUMERICAL METHODS; UNDERCOOLING;

ANALYTICAL SOLUTION; ENTHALPY BASED MODEL; RUBINSTEIN BINARY-ALLOY PROBLEM;

BINARY ALLOYS;

BINARY ALLOYS; ENTHALPY; HEAT TRANSFER; MASS TRANSFER; NUMERICAL METHODS; UNDERCOOLING;

EID: 37749011166     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2007.04.020     Document Type: Article

References (28)

1. Crank J. Free and Moving Boundary Problems (1984), Claendon Press, Oxford
2. Voller V.R. Numerical methods for phase-change problems. In: Minkowycz W.J., Sparrow E.M., and Murthy J.Y. (Eds). Handbook of Numerical Heat Transfer (2006), John Wiley, New York 593-622
3. Eyres N.R., Hartree D.R., Ingham J., Jackson R., Sarjant R.J., and Wagstaff S.M. The calculation of variable heat flow in solids. Phil. Trans. R. Soc. A 240 (1946) 1-57
4. Price P.H., and Slack M.R. The effect of latent heat on numerical solutions of the heat flow equation. Br. J. Appl. Phys 5 (1954) 285-287
5. Voller V., and Cross M. Accurate solutions of moving boundary problems using the enthalpy method. Int. J. Heat Mass Transfer 24 (1981) 545-556
6. Date A.W. Novel strongly implicit formulation for multidimensional Stefan problems. Numer. Heat Transfer B 27 (1992) 231-251
7. Lacroix M., and Voller V.R. Finite difference solutions of solidification phase change problems: transformed vs. fixed grids. Numer. Heat Transfer 17 (1990) 25-42
8. Giffith R., and Nassersharif B. Comparison of one-dimensional interface-following and enthalpy methods for the numerical solution of phase change. Numer. Heat Transfer (B) 18 (1990) 169-187
9. Caldwell J., and Chen C.-C. Numerical solutions of the Stefan problem by the enthalpy methods and the heat balance integral method. Numer. Heat Transfer B 33 (1998) 99-117
10. Voller V.R., Mouchmov A., and Cross M. An explicit method for coupling temperature and concentration fields in solidification models. Appl. Math. Model. 28 (2004) 79-94
11. Ganguly S., and Chakraborty S. A generalized enthalpy-based macro model for ternary alloy solidification simulations. Numer. Heat Transfer B 51 (2007) 293-313
12. Rubinstein L. The Stefan Problem. Translations of Math. Monographs vol. 27 (1971), American Mathematical Society, Providence
13. Alexiades V., and Solomon A.D. Mathematical Modeling of Melting and Freezing Processes (1984), Hemisphere, Washington pp. 106-109
14. Crowley A.B., and Ockendon J.R. On the numerical solution of an alloy solidification problem. Int. J. Heat Mass Transfer 22 (1979) 941-947
15. Voller V.R. An implicit enthalpy solution for phase change problems: with application to a binary alloy solidification. Appl. Math. Model. 11 (1987) 110-116
16. Wilson D.G., Solomon A.D., and Alexiades V. A model of binary alloy solidification. Int. J. Numer. Meth. Eng. 20 (1984) 1084-1967
17. Kurz W., and Fisher D.J. Fundamentals of Solidification (1986), Trans Tech Publishing, Switzerland pp. 53-54
18. Mullins W.W., and Sekerka R.F. Stability of a planar interface during solidification of a dilute binary alloy. J. Appl. Phys. 35 (1964) 444-451
19. V.R. Voller, An enthalpy method for modeling dendritic growth in a binary alloy, Int. J. Heat and Mass Transfer, in press, doi:10.1016/j.ijheatmasstransfer.2007.04.025.
20. Voller V.R. A similarity solution for solidification of an under-cooled binary alloy. Int. J. Heat Mass Transfer 49 (2006) 1981-1985
21. Carslaw H., and Jaeger J. Conduction of Heat in Solids. second ed. (1959), Clarendon Press, Oxford
22. Voller V.R. Numerical treatment of rapidly changing and discontinuous conductivities. Int. J. Heat Mass Transfer 44 (2001) 4553-4556
23. Ramirez J.C., Beckermann C., Karma A., and Diepers H.-J. Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion. Phys. Rev. E 69 (2004)
24. Zhao P., Vénere M., Heinrich J.C., and Poirier D.R. Modeling dendritic growth of a binary alloy. J. Computat. Phys. 188 (2003) 434-461
25. Voller V.R. An enthalpy based scheme for simulating dendritic growth. In: Gandin C.-A., and Bellet M. (Eds). Modeling of Casting, Welding and Advanced Solidification Processes-XI (2006), TMS, Warrendale 465-472
26. Voller V.R., and Murfield N. Application of an enthalpy method for dendritic solidification. In: Novak A.J., et al. (Ed). Numerical Heat Transfer 2005 (2005), Institute of Thermal Technology, Poland 379-386
27. Chatterjee D., and Chakraborty S. A hybrid lattice Boltzmann model for solid-liquid phase transition in presence of fluid flow. Phys. Lett. A 351 (2006) 359-367
28. Pal D., Bhattacharya J., Dutta P., and Chakraborty S. An enthalpy model for simulation of dendritic growth. Numer. Heat Transfer B 50 (2006) 59-78