On an integral formulation for moving boundary problems
Authors:
Jeffrey N. Dewynne and James M. Hill
Journal:
Quart. Appl. Math. 41 (1984), 443-455
MSC:
Primary 80A20; Secondary 35R35
DOI:
https://doi.org/10.1090/qam/724055
MathSciNet review:
724055
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Abstract: The classical moving boundary problems arising in the freezing or chemical reaction of spheres, cylinders and slabs are considered. An integral method is employed to formally effect the integration of the motion of the moving boundary. This formal integration permits upper and lower bounds to be deduced for the motion and in particular simple upper and lower bounds are established for the time to complete freezing or reaction (that is, when the moving boundary reaches the centre of the sphere or cylinder). In addition an improved second upper bound on the motion is achieved by demonstrating that the dimensionless temperature or concentration is bounded above by the standard pseudo steady state approximation. The use of the integral formulation as an iterative scheme and the generalisations for a time dependent surface condition and a non nlinear diffusivity are also briefly considered.
- Gregory B. Davis and James M. Hill, A moving boundary problem for the sphere, IMA J. Appl. Math. 29 (1982), no. 1, 99–111. MR 667784, DOI https://doi.org/10.1093/imamat/29.1.99
T. R. Goodman, The heat-balance method and its application to problems involving a change of phase, Trans. ASME 80 (1958), 335–342
R. I. Pedroso and G. A. Domoto, Perturbation solutions for spherical solidification of saturated liquids, Trans. ASME 95 (1973), 42–46
R. I. Pedroso and G. A. Domoto, Inward spherical solidification solution by the method of strained coordinates, Int. J. Heat Mass Transfer 16 (1973), 1037–1043
D. S. Riley, F. T. Smith and G. Poots, The inward solidification of spheres and circular cylinders, Int. J. Heat Mass Transfer 17 (1974), 1507–1516
J. M. Savino and R. Siegel, An analytical solution for solidification of a moving warm liquid onto an isothermal cold wall, Int. J. Heat Mass Transfer 12 (1969), 803–809
Y. P. Shih and T. C. Chou, Analytical solutions for freezing a saturated liquid inside or outside spheres, Chem. Engng. Sci. 26 (1971), 1787–1793
Y. P. Shih and S. Y. Tsay, Analytical solutions for freezing a saturated liquid inside or outside cylinders, Chem. Engng. Sci. 26 (1971), 809–816
- A. D. Solomon, V. Alexiades, and D. G. Wilson, The Stefan problem with a convective boundary condition, Quart. Appl. Math. 40 (1982/83), no. 2, 203–217. MR 666675, DOI https://doi.org/10.1090/S0033-569X-1982-0666675-6
A. M. Soward, A unified approach to Stefan’s problem for spheres and cylinders, Proc. R. Soc. Lond. A373 (1980), 131–147
K. Stewartson and R. T. Waechter, On Stefan’s problem for spheres, Proc. R. Soc. Lond. A348 (1976), 415–426
L. C. Tao, Generalised numerical solutions of freezing a saturated liquid in cylinders and spheres, A. I. Ch. E. Jl. 13 (1967), 165–169
T. G. Theofanous and H. C. Lim, An approximate analytical solution for non-planar moving boundary problems, Chem. Engng. Sci. 26 (1971), 1297–1300
G. B. Davis and J. M. Hill, The classical moving boundary problem for the sphere, IMA J. Appl. Math. 29 (1982), 99–111
T. R. Goodman, The heat-balance method and its application to problems involving a change of phase, Trans. ASME 80 (1958), 335–342
R. I. Pedroso and G. A. Domoto, Perturbation solutions for spherical solidification of saturated liquids, Trans. ASME 95 (1973), 42–46
R. I. Pedroso and G. A. Domoto, Inward spherical solidification solution by the method of strained coordinates, Int. J. Heat Mass Transfer 16 (1973), 1037–1043
D. S. Riley, F. T. Smith and G. Poots, The inward solidification of spheres and circular cylinders, Int. J. Heat Mass Transfer 17 (1974), 1507–1516
J. M. Savino and R. Siegel, An analytical solution for solidification of a moving warm liquid onto an isothermal cold wall, Int. J. Heat Mass Transfer 12 (1969), 803–809
Y. P. Shih and T. C. Chou, Analytical solutions for freezing a saturated liquid inside or outside spheres, Chem. Engng. Sci. 26 (1971), 1787–1793
Y. P. Shih and S. Y. Tsay, Analytical solutions for freezing a saturated liquid inside or outside cylinders, Chem. Engng. Sci. 26 (1971), 809–816
A. D. Solomon, V. Alexiades and D. G. Wilson, The Stefan problem with a convective boundary condition, Quart. Appl. Math. 40 (1982), 203–217
A. M. Soward, A unified approach to Stefan’s problem for spheres and cylinders, Proc. R. Soc. Lond. A373 (1980), 131–147
K. Stewartson and R. T. Waechter, On Stefan’s problem for spheres, Proc. R. Soc. Lond. A348 (1976), 415–426
L. C. Tao, Generalised numerical solutions of freezing a saturated liquid in cylinders and spheres, A. I. Ch. E. Jl. 13 (1967), 165–169
T. G. Theofanous and H. C. Lim, An approximate analytical solution for non-planar moving boundary problems, Chem. Engng. Sci. 26 (1971), 1297–1300
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Article copyright:
© Copyright 1984
American Mathematical Society
