A Fixed Grid Finite Control Volume Model for the Phase Change Heat Conduction Problems with a Single-Point Predictor-Corrector Algorithm

Sin Kim; Min Chan Kim; Won-Gee Chun

Korean Journal of Chemical Engineering, Vol.18, No.1, 40-45, January, 2001

Sin Kim, Min Chan Kim^{1, †}, and Won-Gee Chun

Department of Nuclear and Energy Engineering, Cheju National University, Cheju 690-756, Korea
¹Department of Chemical Engineering, Cheju National University, Cheju 690-756, Korea

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A numerical scheme based on the enthalpy method is applied to one-dimensional Stefan problems. The discretization equation is derived based on the finite control volume method. To improve the convergence rate, a simple and cost-effective single-point predictor-corrector algorithm is proposed. Usefulness of the present approach is discussed by means of various solidification problems.

Keywords:One-Dimensional Stefan Problem;Fixed Grid Method;Enthalpy Formulation;Source Update Method

[References]

Carslaw HS, Jaeger JC, "Conduction of Heat in Solids," Chap. 11, 2nd ed., Oxford Univ. Press, Oxford (1959)
Choi JC, Kim SD, Han GY, Korean J. Chem. Eng., 12(2), 258 (1995)
Crank J, "Free and Moving Boundary Problems," Oxford Univ. Press, Oxford (1984)
Davey K, Rosindale I, Int. J. Numer. Methods Eng., 46, 315 (1999)
Ding Z, "Modeling of Bulk Evaporation and Condensation with internal Heating at Various Gravity Level," Ph.D. Dissertation, Dept. of Mech. Eng. Univ. of Florida (1995)
Fachinotti VD, Cardona A, Huespe AE, Int. J. Numer. Methods Eng., 44, 1863 (1999)
Kruz W, Fisher DJ, "Fundamentals of Solidification," 2nd ed., Trans Tech Pub., Switzerland (1989)
Patankar SV, "Numerical Heat Transfer and Fluid Flow," Hemisphere, Washington DC (1980)
Voller VR, "An Overview of Numerical Methods for Solving Phase Change Problems," Advances in Numerical Heat Transfer (edited by WJ Minkowycz and EM Sparrow), Taylor and Francis, Washington DC, 1, 341 (1997)
Voller VR, Numer. Heat Transf. B-Fundam., 17, 155 (1990)

[Referenced By]

[Related Articles]

[1] Carslaw HS, Jaeger JC, "Conduction of Heat in Solids," Chap. 11, 2nd ed., Oxford Univ. Press, Oxford (1959)

[2] Choi JC, Kim SD, Han GY, Korean J. Chem. Eng., 12(2), 258 (1995)

[3] Crank J, "Free and Moving Boundary Problems," Oxford Univ. Press, Oxford (1984)

[4] Davey K, Rosindale I, Int. J. Numer. Methods Eng., 46, 315 (1999)

[5] Ding Z, "Modeling of Bulk Evaporation and Condensation with internal Heating at Various Gravity Level," Ph.D. Dissertation, Dept. of Mech. Eng. Univ. of Florida (1995)

[6] Fachinotti VD, Cardona A, Huespe AE, Int. J. Numer. Methods Eng., 44, 1863 (1999)

[7] Kruz W, Fisher DJ, "Fundamentals of Solidification," 2nd ed., Trans Tech Pub., Switzerland (1989)

[8] Patankar SV, "Numerical Heat Transfer and Fluid Flow," Hemisphere, Washington DC (1980)

[9] Voller VR, "An Overview of Numerical Methods for Solving Phase Change Problems," Advances in Numerical Heat Transfer (edited by WJ Minkowycz and EM Sparrow), Taylor and Francis, Washington DC, 1, 341 (1997)

[10] Voller VR, Numer. Heat Transf. B-Fundam., 17, 155 (1990)