Abstract
Three classical problems associated with the ordinary diffusion equation concern the temperature in (1) a half-space with clamped heat flux at the free face, (2) a half-space with clamped temperature at the free face, and (3) an infinite medium with a pulsed plane heat source. These problems are also important for the nonlinear diffusion equation based on the Gorter-Mellink relation, which describes heat transport in superfluid helium. A similarity solution to problem (1) , the champed-flux problem, has already been found1 and compared, with goou agreement, with experimental data of van Sciver.2 [A similarity solution is one in which the profiles of temperature rise AT versus distance Z at different times t can be obtained from one another by suitable (different) stretching of the temperature and distance axes.] In this paper, I give similarity solutions in analytic form to problems (2) and (3) , the clamped-temperature and pulsed-source problems.
Research sponsored by the Office of Fusion Energy, U.S. Department of Energy, under contract W-7405-eng-26 with the Union Carbide Corporation.
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References
L. Dresner, Transient heat transfer in superfluid helium in Advances in Cryogenic Engineering, Vol. 27, Plenum Press, New York (1982), p. 411.
S. W. van Sciver, Transient heat transport in He-II, Cryogenics 19:385 (1979).
P. Seyfert, J. Lafferranderie, and G. Claudet, Time-dependent heat transport in subcooled superfluid helium, Cryogenics 22:401 (1982).
J. C. Lottin and S. W. van Sciver, Heat transport mechanisms in a 2. 3-meter-long cooling loop containing He-II, in “Proceedings of the Ninth International Cryogenic Engineering Conference, Kobe, Japan, May 11–14, 1982,” Butterworth, Guildford, Surrey (1982), p. 269.
L. Dresner, “Similarity Solutions of Nonlinear Partial Differential Equations,” Pitman Publishing (to be published).
M. O. Hoenig, Internally cooled, cabled superconductors cooled with He-II, in “Proceedings of the Saclay Workshop, November 16–19, 1981,” International Institute of Refrigeration, Paris, France (1982), p. 301.
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© 1984 Plenum Press, New York
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Dresner, L. (1984). Transient Heat Transfer in Superfluid Helium — Part II. In: Fast, R.W. (eds) Advances in Cryogenic Engineering. Advances in Cryogenic Engineering, vol 29. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-9865-3_37
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DOI: https://doi.org/10.1007/978-1-4613-9865-3_37
Publisher Name: Springer, Boston, MA
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