On heat conduction with phase change: Accurate explicit numerical method

Journal of Applied Fluid Mechanics

Volumn 5, Issue 1, 2012, Pages 105-112

  Sadoun, N ^a,b   Si Ahmed, E K ^a,c   Legrand, J ^c  

^a UNIVERSITY OF SCIENCES AND TECHNOLOGY HOUARI BOUMEDIENE   (Algeria)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^c UNIVERSITÉ DE NANTES   (France)

Author keywords

Moving boundary; Numerical method; Stefan; Variable space step

Indexed keywords

EID: 84856842783     PISSN: 17353572     EISSN: 17353645     Source Type: Journal    
DOI: None     Document Type: Article

References (41)

1. Bell, G. E., (1978). A refinement of the heat balance integral method applied to melting problem. Int. J. Heat Mass Transfer, 21, 1357-1362
2. Caldwell, J. and Y.Y. Kwan, (2005). Starting solutions for the boundary immobilisation method. Commun. Numer. Meth. Eng, 21, 289-295.
3. Caldwell, J. and C.C. Chan (2000). Spherical solidification by enthalpy method and the heat balance integral method. Appl. Math. Modelling, 24, 45-53
4. Carslaw, H.S. and J.C. Jaeger (1959). Conduction Of Heat In Solids. Second Edn. Oxford Clarendon Press, Oxford.
5. Crank, J. (1957). Two methods for the numerical solution of moving-boundary problems in diffusion and heat flow. Quart. J. Mech. Math., 10, 220-231.
6. Elmas, M. (1970). On the solidification of the warm liquid flowing over a cold wall. Int. J. Heat Mass Transfer, 13, 1060-1062
7. Elsen, A. and S. Kutluay (2004). A numerical solution of the Stefan problem with a Neumann-type boundary condition by enthalpy method. Appl. Math. Comput., 148, 321-329.
8. El-Genk, M. S. and Cronenberg, A. W. (1979). Some Improvements to the solution of Stefan likeproblems, Int. J. Heat Mass Transfer, 22, 167-17.
9. El-Genk, M.S. (1978). Improvements to the Solution of Stefan-like Freezing and Melting Problems, with Application to LMFBR Safety Analysis, Approximate Analysis of Heat Transfer in Transpired Boundary Layers with Effects of Prandtl Number. Ph.D. Dissertation, University of New Mexico, Albuquerque NM, USA
10. Fox, L. (1975). What are the best numerical methods? Moving Boundary Problems In Heat Flow And Diffusion. Ed. Ockendon J. R., Hodgkins W. R., Clarendon Press, Oxford, UK, 210-241.
11. Goodman, T.R. (1964). Application of integral methods to transient nonlinear heat transfer. Advances In Heat transfer, Irvine T.F. Jr. & Hartnett J P, eds., New York: Academic Press, Vol. I, 51-122.
12. Goodman, T.R. (1961). The heat balance integral -further considerations and refinements. Trans. ASME J. of Heat Transfer, 83, 83-88.
13. Hamill, T. D. and S.G. Bankoff (1963). Maximum and minimum bounds of freezing-melting rates with time dependent boundary conditions. A.I.Ch.E. Journal, 9, 741-744.
14. Hristov, J. (2007). An inverse Stefan problem relevant to boilover: Heat balance integral solutions and analysis. Thermal Science, 11, 141-160.
15. Kutluay, S., A.R Bahadir and A. Özdeş (1997)., The numerical solution of one-classical Stefan problem. J. Comput. Appl. Math., 81, 135-144.
16. Kutluay, S. and A. Elsen (2004). An isotherm migration formulation for one-phase Stefan problem with time dependent Neumann condition. Appl. Math. Comput., 150, 59-67.
17. Kutluay, S. (2005). Numerical schemes for onedimensional Stefan-like problems with a forcing term. Appl. Math. Comput., 168, 1159-1168
18. Kutluay, S., A.S. Wood and A. Esen (2006). A heat balance integral solution the termistor problem with a modified electrical conductivity. Appl. Math. Modelling, 30, 386-394
19. Langford D., The heat balance integral method, Int. J. Heat Mass Transfer, 16, 2424-2428 (1973).
20. Mennig, J. and M.N. Özişik (1985). Coupled integral approach for solving melting and solidification, Int. J. Heat Mass Transfer, 28, 1481-1485
21. Mitchell S.L. and T.G. Myers (2008). Approximate methods for one-dimensional solidification from an incoming fluid. Appl. Math. Comput., doi: 10.1016/j.amc.2008.02.031.
22. Mosally, F., A.S. Wood and A. Al-Fhaid (2005). An exponential heat balance integral method. Appl. Math. Comput., 29, 903-9012
23. Murray, W.D. and F. Landis (1959). Numerical and machine solutions of the transient heat conduction problems involving melting or freezing. J. Heat transfer, 81, 106-112.
24. Noble, B. (1975). Heat balance methods in melting problems. Moving Boundary Problems in Heat Flow and Diffusion, Ed. Ockendon J. R., Hodgkins W. R., Clarendon Press, Oxford, UK, 208-209.
25. Poots, G. (1962a). On the application of integral-methods to the solution of problems involving the solidification of liquids initially at fusion temperature. Int. J. Heat Mass Transfer, 5, 525-531.
26. Poots, G. (1962b). An approximate treatment of a heat conduction problem involving a two-dimensional front. Int. J. Heat Mass Transfer, 5, 339-348
27. Riley, D. S. and P.W. Duck (1976). Application of the heat-balance integral method to the freezing of a cuboid. Int. J. Heat Mass Transfer, 19, 294-296.
28. Sadoun, N. and E.K. Si-Ahmed (1993). On the double integral method for solving Stefan like-problems. Proceedings, First International Thermal and Energy Congress, Marrakesh, Morocco, Vol. 1, 87-91.
29. Sadoun, N. (2006). Contribution à l'Etude du Problème de Solidification - Approche Semi Analytique. Magister Thesis, Faculté de Physique, University of USTHB.
30. Sadoun, N., E.K. Si-Ahmed and J. Legrand. (2006a). A refined exponential heat balance integral method for one-phase Stefan problem. Proceedings, The Second International Conference on Thermal Engineering: Theory and Applications, Ed. Chacha and al., Al-Ain, UAE, 528-532
31. Sadoun, N., E.K. Si-Ahmed and P. Colinet (2006b). On the refined integral method for one-phase Stefan with time-dependent boundary conditions. Appl. Math. Modelling. 30, 531-544
32. Sadoun, N., E.K. Si-Ahmed, P. Colinet and J. Legrand (2009). On the Goodman heat-balance integral method for Stefan like-problems: Further considerations and refinements. Thermal Science, 13, 81-96
33. Sahu, S.K., P.K. Das and S. Bhattacharyya (2006). A comprehensive analysis of conduction-controlled rewetting by the heat balance integral method. Int. J. Heat Mass Transfer., 49, 4978-4986.
34. Savović, S. and J. Caldwell (2003). Finite difference solution of one-dimensional Stefan problem with periodic boundary conditions. Int. J. Heat. Transfer, 46, 2911-2916.
35. Sucec, J. (1979). Extension of modified integral method to boundary conditions of prescribed surface heat flux. Int. J. Heat Mass Transfer, 22, 771-774.
36. Verma, A.K., S. Chandra and B.K. Dhindaw (2004). An alternative fixed grid method for solution of the classical one-phase Stefan problem. Appl. Math. Comput., 158, 573-584
37. Vokov, V.N. and V.K. Li-Orlov (1970). A refinement of the integral method in solving the heat conduction equation. Heat Transfer Sov. Res., 2, 41-47.
38. Voller V. and M. Cross (1981). Accurate solutions of moving boundary problems using the enthalpie method. Int. J. Heat Mass Transfer, 24, 545-556
39. Vujanovic, B. and Dj. Djukic (1972). On one variational principle of Hamilton's type for nonlinear heat transfer problem. Int. J. Heat Mass Transfer, 15, 1111-1123.
40. Wood, A.S. and S. Kutluay (1995). A heat balance integral model for thermistor, Int. J. Heat Mass Transfer, 38, 1831-1840.
41. Zien, T.F. (1976). Approximate analysis of heat transfer in transpired boundary layers with effects of Prandtl number. Int. J. Heat Mass Transfer, 19, 513-521.