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NUMERICAL STUDY OF THE THERMAL STATE OF AN ICE LAYER CONTAINING AIR BUBBLES

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Abstract

The melting of an ice layer with air bubbles on exposure to an artificial thermal radiation source is studied by mathematical modeling within the framework of the one-phase Stefan problem. The radiative part of the problem of radiative-conductive heat transfer in the ice layer is solved numerically by a modified mean flux method taking into account the absorption and scattering of the radiation in the medium and the selectivity of the radiation. The anisotropic scattering of radiation by air bubbles is taken into account using a transport approximation. It is shown that the calculation results are in satisfactory agreement with experimental data.

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REFERENCES

  1. Radiative Thermal Physics of Snow and Ice (Gidrometeoizdat, Leningrad, 1990) [in Russian].

    Google Scholar 

  2. Thermics and Mechanics of Natural Ice (Nauka, Moscow, 1983) [in Russian].

    Google Scholar 

  3. The Physics of Glaciers (Pergamon Press, Oxford, 1981;. Moscow: Mir, 1984).

    Google Scholar 

  4. “Simulation of Radiative Heating of Snow and Ice Coating," Teplofiz. Aeromekh. 25 (5), 797–804 (2018) [Thermophys. Aeromech. 25 (5), 765–772 (2018). DOI: 10.1134/S086986431805013X].

    Article  ADS  Google Scholar 

  5. “On Snowpack Heating by Solar Radiation: A Computational Model," J. Quantitative Spectroscopy Radiative Transfer227, 72–85 (2019).

    Article  ADS  Google Scholar 

  6. L. A. Dombrovsky and A. A. Kokhanovsky, “Solar Heating of Ice Sheets Containing Gas Bubbles," J. Quantitative Spectroscopy Radiative Transfer 250, 106991 (2020).

    Article  Google Scholar 

  7. S. D. Sleptsov, N. A. Rubtsov, and N. A. Savvinova, “Modeling of Ice Heating and Melting in Approximation of the Stefan Problem Considering Radiation," Teplofiz. Aeromekh. 25 (3), 439–446 (2018) [Thermophys. Aeromech. 25 (3), 421–428 (2018). DOI: 10.1134/S0869864318030095].

    Article  ADS  Google Scholar 

  8. S. D. Sleptsov, N. A. Savvinova, and N. A. Rubtsov, “Ice Melting with Allowance for Selective Absorption in the Medium," J. Engng Thermophys. 28 (1), 114–122 (2019).

    Article  Google Scholar 

  9. S. D. Sleptsov and N. A. Savvinova, “Ice Melting under Irradiation by a Selective Heat Source," Teplofiz. Aeromekh. 26 (5), 813–820 (2018) [Thermophys. Aeromech. 26 (5), 761–768 (2019). DOI: 10.1134/S0869864319050135].

    Article  ADS  Google Scholar 

  10. S. D. Sleptsov and N. A. Savvinova, “Computational Study of Non-Stationary Thermal State of an Ice Layer Taking into Account Radiation Scattering," Teplofiz. Aeromekh. 27 (4), 645–652 (2020) [Thermophys. Aeromech. 27 (4), 615—622 (2020). DOI: 10.1134/S0869864320040149].

    Article  ADS  Google Scholar 

  11. N. Seki, M. Sugawara, and S. Fukusaki, “Radiative Melting of Ice Layer Adhering to a Vertical Surface," Wärme- und Stoffübertrag12, 137–144 (1979).

    Article  ADS  Google Scholar 

  12. N. A. Rubtsov, A. M. Timofeev, and N. A. Savvinova, Combined Heat Transfer in Semitransparent Media (Izd. SO RAN, Novosibirsk, 2003) [in Russian].

    Google Scholar 

  13. L. A. Dombrovsky and D. Baillis, Thermal Radiation in Disperse Systems: An Engineering Approach (N. Y.: Begell House, 2010).

    Google Scholar 

  14. L. A. Dombrovsky, “The Use of Transport Approximation and Diffusion-Based Models in Radiative Transfer Calculations," Comput. Thermal Sci. 4 (4), 297–315 (2012).

    Article  Google Scholar 

  15. L. A. Dombrovsky, “Scattering of Radiation and Simple Approaches to Radiative Transfer in Thermal Engineering and Biomedical Applications," in Light Scattering and Radiative Transfer (Springer, 2019), pp. 71–127. (Springer Ser. in Light Scattering; V. 4).

  16. N. M. Ozisik, Radiative Transfer and Interactions with Conduction and Convection (Wiley-Interscience, New York, 1973).

    Google Scholar 

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

    MATH  Google Scholar 

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Correspondence to S. D. Sleptsov.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2021, Vol. 62, No. 3, pp. 118-125. https://doi.org/10.15372/PMTF20210311.

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Sleptsov, S.D., Savvinova, N.A. & Grishin, M.A. NUMERICAL STUDY OF THE THERMAL STATE OF AN ICE LAYER CONTAINING AIR BUBBLES. J Appl Mech Tech Phy 62, 451–457 (2021). https://doi.org/10.1134/S0021894421030111

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  • DOI: https://doi.org/10.1134/S0021894421030111

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