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.
- Carlo Cattaneo, Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena 3 (1949), 83–101 (Italian). MR 0032898
W. A. Scheffler, Non-equilibrium statistical mechanics of irreversible processes and engineering applications, Ph.D. Thesis, U. of Minn., 1971
M. Chester, Second sound in solids, Phys. Rev. 131, 2013–2015 (1963).
G. Grioli, Sulla propagazione di onde termomeccaniche nei continui, Rend. Sc. Fis. Mat. Nat. Acc. Lincei 67, 426–432 (1979)
M. N. Özisik, Heat conduction, Wiley, New York, 1980
M. J. Maurer and H. A. Thompson, Non-Fourier effects at high heat fluxes. Trans. ASME, J. Heat Transfer. 95, 284–286 (1973)
M. Primicerio, Problemi di diffusione a frontiera libera. Boll. UMI 18A, 11–68 (1981)
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
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
C. Cattaneo, Sulla conduzione del colore, Atti Sem. Mat. Fis. Univ. Modena, 3, 3–21 (1948/49)
W. A. Scheffler, Non-equilibrium statistical mechanics of irreversible processes and engineering applications, Ph.D. Thesis, U. of Minn., 1971
M. Chester, Second sound in solids, Phys. Rev. 131, 2013–2015 (1963).
G. Grioli, Sulla propagazione di onde termomeccaniche nei continui, Rend. Sc. Fis. Mat. Nat. Acc. Lincei 67, 426–432 (1979)
M. N. Özisik, Heat conduction, Wiley, New York, 1980
M. J. Maurer and H. A. Thompson, Non-Fourier effects at high heat fluxes. Trans. ASME, J. Heat Transfer. 95, 284–286 (1973)
M. Primicerio, Problemi di diffusione a frontiera libera. Boll. UMI 18A, 11–68 (1981)
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
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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Article copyright:
© Copyright 1983
American Mathematical Society
