Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



A hyperbolic Stefan problem

Authors: L. M. De Socio and G. Gualtieri
Journal: Quart. Appl. Math. 41 (1983), 253-259
MSC: Primary 80A20; Secondary 35K05
DOI: https://doi.org/10.1090/qam/719509
MathSciNet review: 719509
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Abstract: Heat conduction is considered in a semi-infinite solid subjected to a high step change in surface heat flux, such that melting occurs. A time-dependent relaxation model for the energy flux is assumed, leading to a non-Fourier, non-linear equation for the thermal field, which is solved under suitable conditions on the interface displacement.

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

  • [1] Carlo Cattaneo, Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena 3 (1949), 83–101 (Italian). MR 0032898
  • [2] W. A. Scheffler, Non-equilibrium statistical mechanics of irreversible processes and engineering applications, Ph.D. Thesis, U. of Minn., 1971
  • [3] M. Chester, Second sound in solids, Phys. Rev. 131, 2013-2015 (1963).
  • [4] G. Grioli, Sulla propagazione di onde termomeccaniche nei continui, Rend. Sc. Fis. Mat. Nat. Acc. Lincei 67, 426-432 (1979)
  • [5] M. N. Özisik, Heat conduction, Wiley, New York, 1980
  • [6] M. J. Maurer and H. A. Thompson, Non-Fourier effects at high heat fluxes. Trans. ASME, J. Heat Transfer. 95, 284-286 (1973)
  • [7] M. Primicerio, Problemi di diffusione a frontiera libera. Boll. UMI 18A, 11-68 (1981)
  • [8] B. Boley, The embedding technique in melting and solidification problems, in Moving Boundaries Problems in Heat Flow and Diffusion, J. R. Ockerdon & W. R. Hodgkins eds., Oxford University Press, New York, 1975
  • [9] J. P. Brazel and E. J. Nolan, Non-Fourier effects in the transmission of heat, Proc. 6th Conference on Thermal Conducitivity, Dayton, 237-254, October 1966

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DOI: https://doi.org/10.1090/qam/719509
Article copyright: © Copyright 1983 American Mathematical Society

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