Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Approximate analytical solution of a Stefan's problem in a finite domain


Author: Shunsuke Takagi
Journal: Quart. Appl. Math. 46 (1988), 245-266
MSC: Primary 35R35; Secondary 35K05, 73B30, 80A20
DOI: https://doi.org/10.1090/qam/950600
MathSciNet review: 950600
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A Stefan's problem in a finite domain may be given an approximate analytical solution. An example is shown with constant boundary and initial conditions. The solution is initially that of a semi-infinite domain, transits through infinitely many intermediate stage solutions, and finally becomes stationary. The solution is exact in the initial stage and also at the steady final stage, but approximate at the intermediate stages.


References [Enhancements On Off] (What's this?)

  • [1] I. G. Portnov, Exact solution of freezing problem with arbitrary temperature variation on fixed boundary, Soviet Phys. Dokl. 7, 186 (1962)
  • [2] F. Jackson, The solution of problems involving the melting and freezing of finite slabs by a method due to Portnov, Proc. Edinburgh Math. Soc. 14 (2), 109 (1964) MR 0177639
  • [3] K. O. Westphal, Series solution of freezing problem with the fixed surface radiation in a medium of arbitrary varying temperature, Int. J. Heat Mass Trans. 10, 195-205 (1967)
  • [4] L. N. Tao, The Stefan problem with arbitrary initial and boundary conditions, Quart. Appl. Math. 36, 223-233 (1978) MR 508769
  • [5] L. N. Tao, The solidification problems including the density jump at the moving boundary, Quart. J. Mech. Appl. Math. 32, 175-185 (1979) MR 537351
  • [6] L. N. Tao, The analyticity of solutions of the Stefan problem, Arch. Rat. Mech. Anal. 72, 285-301 (1980) MR 549645
  • [7] H. G. Landau, Heat conduction in a melting solid, Quart. Appl. Math. 8, 81-94 (1950) MR 0033441
  • [8] H. S. Carslaw and J. C. Jaeger, Conduction of heat in solids, Oxford University Press, New York, 1959 MR 0022294
  • [9] D. V. Widder, The heat equation, Academic Press, New York, 1975 MR 0466967
  • [10] I. M. Gel'fand and G. E. Shilov, Generalized functions, Vol. 1, Academic Press, New York, 1964 MR 0166596
  • [11] B. A. Boley, The embedding technique in melting and solidification problems, In J. R. Ockendon and W. R. Hodgkins (Eds.), Moving boundary problems in heat flow and diffusion, 150-172, Clarendon Press, Oxford, 1975
  • [12] C. Jordan, Calculus of finite difference, Budapest, 1939
  • [13] M. Abramowitz and I. Stegun (Eds.), Handbook of mathematical functions, AMS 55, NBS, Washington, D. C., 1964 MR 0167642
  • [14] A. M. Ostrowski, Solutions of equations and systems of equations (Second Edition), Academic Press, 1966
  • [15] J. R. Rice, Numerical methods, softwares, and analysis: IMSM reference edition, McGraw-Hill, New York, 1983
  • [16] W. B. Jones and W. J. Thron, Continued fractions, analytic theory and applications, Addison-Wesley Pub. Co., Reading, Mass., 1980 MR 595864
  • [17] J. F. Hart, et al., Computer approximations, John Wiley & Sons, Inc., New York, 1968

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35R35, 35K05, 73B30, 80A20

Retrieve articles in all journals with MSC: 35R35, 35K05, 73B30, 80A20


Additional Information

DOI: https://doi.org/10.1090/qam/950600
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society