Analytic solution of the Stefan problem in finite mediums
Authors:
A. Kar and J. Mazumder
Journal:
Quart. Appl. Math. 52 (1994), 49-58
MSC:
Primary 80A22; Secondary 35C10, 35R35
DOI:
https://doi.org/10.1090/qam/1262318
MathSciNet review:
MR1262318
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Abstract: The classical Stefan problem is considered in this paper for finite mediums with Dirichlet boundary conditions. Analytic solutions for the temperature distributions and the location of the moving interface are obtained by using Lie group theory and the superposition principle. The existence of analytically exact solutions is established by proving the convergence of the solution.
A. Kar and J. Mazumder, One-dimensional diffusion model for extended solid solution in laser cladding, J. Appl. Phys. 61, 2645–2655 (1987)
A. Kar and J. Mazumder, One-dimensional finite-medium diffusion model for extended solid solution in laser cladding of H f on nickel, Acta Metall. 36, 701–712 (1988)
A. Kar and J. Mazumder, Extended solid solution and nonequilibrium phase diagram for Ni-Al alloy formed during laser cladding, Met. Trans. A 20A, 363–371 (1989)
L. N. Tao, The Stefan problem of a polymorphous material, J. Appl. Mech. 46, 789–794 (1979)
L. N. Tao, On solidification of a binary alloy, Quart. J. Mech. Appl. Math. 33, 211–225 (1980)
L. N. Tao, Solidification of a binary mixture with arbitrary heat flux and initial conditions, Arch. Rat. Mech. Anal. 76, 167–181 (1981)
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed., Oxford Univ. Press, 1959
M. N. Özisik, Heat Condition, John Wiley and Sons, New York, 1980
L. N. Tao, The Stefan problem with arbitrary initial and boundary conditions, Quart. Appl. Math. 36, 223–233 (1978)
L. V. Ovsiannikov, Group Analysis of Differential Equations, translation edited by W. F. Ames, Academic Press, New York, 1982, pp. 68–73
G. W. Bluman and G. D. Cole, Similarity Methods for Differential Equations, Springer, New York, 1974, p. 211
M. Abramowitz and I. A. Stegun (editors), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, 1972, p. 299, p. 823
D. V. Widder, The Heat Equation, Academic Press, New York, 1975, pp. 169–194
A. Kar and J. Mazumder, One-dimensional diffusion model for extended solid solution in laser cladding, J. Appl. Phys. 61, 2645–2655 (1987)
A. Kar and J. Mazumder, One-dimensional finite-medium diffusion model for extended solid solution in laser cladding of H f on nickel, Acta Metall. 36, 701–712 (1988)
A. Kar and J. Mazumder, Extended solid solution and nonequilibrium phase diagram for Ni-Al alloy formed during laser cladding, Met. Trans. A 20A, 363–371 (1989)
L. N. Tao, The Stefan problem of a polymorphous material, J. Appl. Mech. 46, 789–794 (1979)
L. N. Tao, On solidification of a binary alloy, Quart. J. Mech. Appl. Math. 33, 211–225 (1980)
L. N. Tao, Solidification of a binary mixture with arbitrary heat flux and initial conditions, Arch. Rat. Mech. Anal. 76, 167–181 (1981)
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed., Oxford Univ. Press, 1959
M. N. Özisik, Heat Condition, John Wiley and Sons, New York, 1980
L. N. Tao, The Stefan problem with arbitrary initial and boundary conditions, Quart. Appl. Math. 36, 223–233 (1978)
L. V. Ovsiannikov, Group Analysis of Differential Equations, translation edited by W. F. Ames, Academic Press, New York, 1982, pp. 68–73
G. W. Bluman and G. D. Cole, Similarity Methods for Differential Equations, Springer, New York, 1974, p. 211
M. Abramowitz and I. A. Stegun (editors), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, 1972, p. 299, p. 823
D. V. Widder, The Heat Equation, Academic Press, New York, 1975, pp. 169–194
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Article copyright:
© Copyright 1994
American Mathematical Society
