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Numerical modeling of the single-phase Stefan problem in a layer with transparent and semitransparent boundaries

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Abstract

Numerical modeling of the single-phase Stefan problem in a semitransparent layer with transparent, nonabsorbing, and partially radiation-absorbing boundaries is performed. It is shown that at low temperatures of the medium, convection is a determining factor on the boundary of the irradiated sample, and at high temperatures, radiation is predominant. The absence of absorption on the boundaries of the layer leads to acceleration of the heating of the plate and considerable deceleration of melting processes.

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References

  1. V. Le Dez, F. Yousefian, R. Vaillon, et al., “Problem de Stefan direct dans un milieu semitransparent gris,” J. Phys. France., Ser. 3, 6, 373–390 (1996).

    Article  Google Scholar 

  2. H. G. Landau, “Heat conduction in a melting solid,” Quart. Appl. Math., 8, 81–94 (1950).

    MATH  MathSciNet  Google Scholar 

  3. N. A. Rubtsov, N. A. Savvinova, and S. D. Sleptsov, “Single-phase Stefan problem for a semitransparent medium with allowance for radiation reflection,” Teplofiz. Aéromekh., 10, No. 2, 255–264 (2003).

    Google Scholar 

  4. N. A. Rubtsov, A. M. Timofeev, and N. N. Ponomarev, “On the behavior of the transfer coefficients in the direct differential methods of the theory of radiative heat transfer in scattering media,” Izv. Sib. Otd. Akad. Nauk SSSR, Ser. Tekh. Nauk, 5, No. 18, 3–8 (1987).

    Google Scholar 

  5. N. A. Rubtsov and S. D. Sleptsov, “E.ect of boundary conditions on unsteady radiative-conductive heat transfer in a semitransparent layer,” Teplofiz. Aéromekh., 12, No. 1, 95–103 (2005).

    Google Scholar 

  6. N. A. Rubtsov, Heat Transfer by Radiation in Continuous Media [in Russian], Nauka, Novosibirsk (1984).

    Google Scholar 

  7. N. A. Rubtsov, A. M. Timofeev, and N. A. Savvinova, Combined Heat Transfer in Semitransparent Media [in Russian], Izv. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (2003).

    Google Scholar 

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 84–91, May–June, 2006.

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Rubtsov, N.A., Sleptsov, S.D. & Savvinova, N.A. Numerical modeling of the single-phase Stefan problem in a layer with transparent and semitransparent boundaries. J Appl Mech Tech Phys 47, 377–383 (2006). https://doi.org/10.1007/s10808-006-0065-5

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  • DOI: https://doi.org/10.1007/s10808-006-0065-5

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