Nodal integral and finite difference solution of one-dimensional Stefan problem

Journal of Heat Transfer

Volumn 125, Issue 3, 2003, Pages 523-527

  Caldwell, James ^a   Savović, Svetislav ^a   Kwan, Yuen Yick ^a  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Finite difference; Heat transfer; Melting; Moving boundaries; Numerical methods; Phase change

Indexed keywords

BOUNDARY CONDITIONS; FINITE DIFFERENCE METHOD; TEMPERATURE DISTRIBUTION; VELOCITY;

NODAL INTEGRAL;

MELTING;

FINITE DIFFERENCE TECHNIQUE; HEAT TRANSFER; MATHEMATICAL ANALYSIS; MODELING; PHASE CHANGE;

EID: 0038006209     PISSN: 00221481     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.1565091     Document Type: Article

References (16)

1. Crank, J., 1984, Free and Moving Boundary Problems, Clarendon Press, Oxford.
2. Mennig, J., and Özişik, M. N., 1985, "Coupled Integral Equation Approach for Solving Melting or Solidification," Int. J. Heat Mass Transf., 28, pp. 1481-1485.
3. Furzeland, R. M., 1980, "A Comparative Study of Numerical Methods for Moving Boundary Problems," J. Inst. Math. Appl., 5, pp. 411-429.
4. Rizwan-uddin, 1999, "One-Dimensional Phase Change With Periodic Boundary Conditions," Numer. Heat Transfer, Part A, 35, pp. 361-372.
5. Asaithambi, N. S., 1997, "A Variable Time-step Galerkin Method for a One-Dimensional Stefan Problem," Appl. Math. Comput., 81, pp. 189-200.
6. Finn, W. D., and Vorog̀lu, E., 1979, "Finite Element Solution of the Stefan Problem," in The Mathematics of Finite Elements and Applications, J. R. Whiteman, ed., MAFELAP 1978, Academic Press, New York.
7. Asaithambi, N. S., 1992, "A Galerkin Method for Stefan Problems," Appl. Math. Comput., 52, pp. 239-250.
8. Černý, R., and Přikryl, P., 1999, "Numerical Solution of a Stefan-Like Problem in Laser Processing of Semiconducting Alloys," Math. Comput. Simul., 50, pp. 165-173.
9. Gupta, R. S., and Kumar, D., 1980, "A Modified Variale Time Step Method for the One-Dimensional Stefan Problem," Comput. Methods Appl. Mech. Eng., 23, pp. 101-108.
10. Caldwell, J., and Savović, S., 2002, "Numerical Solution of Stefan Problem by Variable Space Grid Method and Boundary Immobilisation Method," J. Math. Sciences, 13, pp. 67-79.
11. Savović, S., and Caldwell, J., 2002, "Numerical Solution of Stefan Problem with Time Dependent Boundary Conditions by Variable Space Grid Method and Boundary Immobilisation Method," submitted to Numer. Heat Transfer.
12. Moyano, E. A., and Scarpettini, A., 2000, "Numerical Stability Study and Error Estimation for Two Implicit Schemes in a Moving Boundary Problem," Numer. Methods Partial Differ. Equ., 16, pp. 42-61.
13. Vermolen, F., and Vuik, K., 1998, "A Numerical Method to Compare Dissolution of Second Phases in Ternary Alloys," J. Comput. Appl. Math., 93, pp. 123-143.
14. Rizwa-uddin, 1999, "A Nodal Method for Phase Change Moving Boundary Problems," Int. J. Comput. Fluid Dyn., 11, pp. 211-221.
15. Yao, L. S., and Prusa, J., 1989, "Melting and Freezing," Adv. Heat Transfer, 19, pp. 1-95.
16. Özişik, N., Heat Conduction, 1993, 2nd Edition, Wiley, New York.