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TECHNICAL NOTES

Nodal Integral and Finite Difference Solution of One-Dimensional Stefan Problem

[+] Author and Article Information
James Caldwell, Svetislav Savović, Yuen-Yick Kwan

Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, People’s Republic of China

J. Heat Transfer 125(3), 523-527 (May 20, 2003) (5 pages) doi:10.1115/1.1565091 History: Received July 03, 2002; Revised November 27, 2002; Online May 20, 2003
Copyright © 2003 by ASME
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References

Crank, J., 1984, Free and Moving Boundary Problems, Clarendon Press, Oxford.
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.
Furzeland,  R. M., 1980, “A Comparative Study of Numerical Methods for Moving Boundary Problems,” J. Inst. Math. Appl., 5, pp. 411–429.
Rizwan-uddin  , 1999, “One-Dimensional Phase Change With Periodic Boundary Conditions,” Numer. Heat Transfer, Part A, 35, pp. 361–372.
Asaithambi,  N. S., 1997, “A Variable Time-step Galerkin Method for a One-Dimensional Stefan Problem,” Appl. Math. Comput., 81, pp. 189–200.
Finn, W. D., and Voroġlu, 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.
Asaithambi,  N. S., 1992, “A Galerkin Method for Stefan Problems,” Appl. Math. Comput., 52, pp. 239–250.
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.
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.
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.
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.
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.
Vermolen,  F., and Vuik,  K., 1998, “A Numerical Method to Compute Dissolution of Second Phases in Ternary Alloys,” J. Comput. Appl. Math., 93, pp. 123–143.
Rizwan-uddin  , 1999, “A Nodal Method for Phase Change Moving Boundary Problems,” Int. J. Comput. Fluid Dyn., 11, pp. 211–221.
Yao,  L. S., and Prusa,  J., 1989, “Melting and Freezing,” Adv. Heat Transfer, 19, pp. 1–95.
Özişik, N., Heat Conduction, 1993, 2nd Edition, Wiley, New York.

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