Heat and solute diffusion with a moving interface: a boundary element approach

International Journal of Heat and Mass Transfer

Volumn 41, Issue 16, 1998, Pages 2429-2436

  Zerroukat, M ^a   Power, H ^a   Wrobel, L C ^b  

^a WESSEX INSTITUTE OF TECHNOLOGY   (United Kingdom)

^b BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; PARTIAL DIFFERENTIAL EQUATIONS; THERMAL DIFFUSION;

SOLUTE DIFFUSION;

HEAT TRANSFER;

BOUNDARY ELEMENT METHOD; DIFFUSION; HEAT TRANSFER;

EID: 0032143516     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0017-9310(97)00372-4     Document Type: Article

References (26)

1. 1. Crank, J., Free and Moving Boundary Problems. Oxford Science Publications, Oxford, 1984.
2. 2. Voller, V. R., Swaminathan, C. R. and Thomas, B. G., Fixed grid techniques for phase change problems: a review. Int. J. Numer. Meth. Eng., 1990, 30, 875-898.
3. 3. Crowley, A. B. and Ockendon, J. R., On the numerical solution of an alloy solidification problem. International Journal of Heat and Mass Transfer, 1979, 22, 941-947.
4. 4. Brebbia, C. A., Telles, J. C. and Wrobel, L. C., Boundary Element Techniques: Theory and Applications in Engineering. Springer-Verlag, Berlin, 1984.
5. 5. Wilson, D. G., Solomon, A. D. and Alexiades, V., A model of binary alloy solidification Int. J. Numer. Meth. Eng., 1984, 20, 1067-1084.
6. 6. Zabaras, N. and Mukherjee, S., An analysis of solidification problems by the boundary element method. Int. J. Numer. Meth. Eng., 1987, 24, 1879-1900.
7. 7. Erhun, M. and Advani, S. G., A BEM approach to model heat flow during crystallization. Int. J. Numer. Meth. Eng., 1992, 35, 351-368.
8. 8. O'Neill, K., Boundary integral equation solution of moving boundary phase change problems. Int. J. Numer. Meth. Eng., 1983, 19, 1925-1850.
9. 9. Hsieh, C. K., Choi, C. Y. and Kassab, A. J., Solution of Stefan problems by a boundary element method. In Boundary Element Technology, Vol. 7, ed. C. A. Brebbia and M. S. Ingber. Computational Mechanics Publications. Southampton, and Elsevier, London, 1992. pp. 473-490.
10. 10. Zabaras, N., Mukherjee, S. and Richmond, O., An analysis of inverse heat transfer problems with phase changes using an integral method. Journal of Heat Transfer, 1988, 110, 554-561.
11. 11. Wrobel, L. C., A boundary element solution to Stean's problem. Boundary Elements, Vol. 5, ed. C. A. Brebbia, T. Futagami and M. Tanaka. Computational Mechanics Publications. Southampton, and Springer-Verlag, Berlin, 1983, pp. 173-182.
12. 12. Coleman, C. J., A boundary integral formulation of the Stefan problem. Appl. Math. Modelling, 1986, 10, 445-449.
13. 13. Heinlein, M., Mukherjee, S. and Richmond, O., A boundary element method analysis of temperature fields and stress during solidification. Acta Mechanica, 1986, 59, 59-81.
14. 14. Wrobel, L. C. and Brebbia, C. A., Boundary Elements Methods in Heat Transfer. Computational Mechanics Publications and Elsevier Applied Science, London. 1992.
15. 15. Fehribach, J. D., Analysis and application of continuation method for a self-similar coupled Stefan system. Quart. Appl. Math., 1993, 51, 405-423.
16. 16. Fix, G. J., Numerical methods for ally solidification problems. In Moving Boundary Problems. ed. D. G. Wilson, A. D. Solomon and P. T. Boggs. Academic Press, New York, 1978, pp. 109-128.
17. 17. Solomon, A. D., Alexiades, V. and Wilson, D. G., A numerical simulation of binary alloy solidification. SIAM J. Sci. Stat. Comput., 1985. 6, 911-921.
18. 18. Meyer, G. H., A numerical method of the solidification of binary alloy. International Journal of Heat and Mass Transfer, 1981, 24, 778-781.
19. 19. DeLima-Silva Jr, W., A front tracking boundary element formulation for heat transfer problems with phase changes. Ph.D. thesis, Wessex Institute of Technology, and University of Portsmouth, United Kingdom, 1994.
20. 20. DeLima-Silva Jr, W. and Wrobel, L. C., A front-tracking BEM formulation for one-phase solidification/melting problems. Engineering Analysis with Boundary Element. 1995, 16, 171-182.
21. 21. Demirel, V. and Wang, S., An efficient boundary element method for two-dimensional transient wave propagation problems. Appl. Math. Modelling. 1987, 11, 411-416.
22. 22. Davey, K. and Hinduja, S., An improved procedure for solving transient heat conduction problems using the boundary element method. Int. J. Numer. Meth. Eng., 1989, 28, 2293-2306.
23. 23. Greengard, L. and Strain, J., A fast algorithm for the evaluation of heat potentials. Comm. Pure Appl. Math., 1990, 43, 949-963.
24. 24. Davey, K. and Bounds, S., Source-weighted domain integral approximation for linear transient heat conduction. Int. J. Numer. Meth. Eng., 1996, 39, 1775-1790.
25. 25. Zerroukat, M., A fast boundary element method for time-dependent potential problems. Appl. Math. Modelling, in press.
26. 26. Wilson, D. G., Solomon, A. D. and Alexiades, V., The shortcoming of the explicit solution for the binary alloy solidification problem. Letters Heat Mass Transfer. 1982, 9, 421-428.