Melting conditions for porous heat-generating device with active cooling: approximate analytical solution

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Abstract

In thermal engineering applications (for example, when studying the operating conditions of thermal storage and electrochemical devices), problems often arise related to the phase transition front propagation in thermally stressed elements. This paper considers the solution of a simplified problem of heating element flow cooling. To this end, analytical estimates were obtained for the critical values of heat release intensity corresponding to the onset of melting and complete melting of the porous sample. The results are compared with numerical calculations.

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About the authors

I. G. Donskoy

Melentiev Energy Systems Institute SB RAS

Author for correspondence.
Email: donskoy.chem@mail.ru
Russian Federation, Irkutsk

References

  1. Sarbu I., Sebachievici C. A Comprehensive Review of Thermal Energy Storage // Sustainability. 2018. V. 10. P. 191. doi: 10.3390/su10010191
  2. Mallick S., Gayen D. Thermal behaviour and thermal runaway propagation in lithium-ion battery systems – A critical review // Journal of Energy Storage. 2023. V. 62. P. 106894. doi: 10.1016/j.est.2023.106894
  3. Panchenko S.V., Bobkov V.I., Fedulov A.S., Chernovalova M.V. Mathematical modelling of thermal and physical-chemical processes during sintering // Non-ferrous Metals. 2018. No. 2. P. 50. doi: 10.17580/nfm.2018.02.09
  4. Thevenin P.O., Ersson A.G., Kusar H.M.J., Menon P.G., Jaras S.G. Deactivation of high temperature combustion catalysts // Applied Catalysis A: General. 2001. V. 212. P. 189. doi: 10.1016/S0926-860X(00)00846-2
  5. Puszynski J., Jayaraman V.K., Hlavacek V. A Stefan problem for exothermic non-catalytic reactions // International Journal of Heat and Mass Transfer. 1985. V. 28. No. 6. P. 1237. doi: 10.1016/0017-9310(85)90133-4
  6. Tripathi P., Rao L. Single particle and packed bed combustion characteristics of high ash and high plastic content refuse derived fuel // Fuel. 2022. V. 308. P. 121983. doi: 10.1016/j.fuel.2021.121983
  7. Sajjadi M., Azaiez J. Heat and mass transfer in melting porous media: Stable miscible displacements // International Journal of Heat and Mass Transfer. 2015. V. 88. P. 926. doi: 10.1016/j.ijheatmasstransfer.2015.05.017
  8. Вулис Л.А. Тепловой режим горения. М.-Л.: Государственное энергетическое издательство, 1954. 288 с.
  9. Lutsenko N.A. Numerical modeling of unsteady gas flow through porous heat-evolutional objects with partial closure of the object’s outlet // International Journal of Heat and Mass Transfer. 2014. V. 72. P. 602. doi: 10.1016/j.ijheatmasstransfer.2014.01.046
  10. Саженков С.А. Исследование задачи Дарси-Стефана о фазовых переходах в насыщенном пористом грунте // ПМТФ. 2008. Т. 49. № 4. С. 81.
  11. Barbu V., Ciotir I., Danaila I. Existence and Uniqueness of Solution to the Two-Phase Stefan Problem with Convection // Applied Mathematics & Optimization. 2021. V. 84. P. 123. doi: 10.1007/s00245-021-09764-w
  12. Crepeau J.C., Siahpush A., Spotten B. On the Stefan problem with volumetric energy generation // Heat and Mass Transfer. 2009. V. 46. P. 119. doi: 10.1007/s00231-009-0550-5
  13. Alsulami R.A., Zope T.M., Premnath K., Aljaghtham M. Convectively cooled solidification in phase change materials in different configurations subject to internal heat generation: Quasi-steady analysis // Applied Thermal Engineering. 2023. V. 221. P. 119849. doi: 10.1016/j.applthermaleng.2022.119849
  14. Донской И.Г. Влияние лучистых теплопотерь на условия плавления материала с внутренним тепловыделением // Изв. ВУЗов. Проблемы энергетики. 2024. Т. 26. № 3. С. 173. doi: 10.30724/1998-9903-2024-26-3-173-183
  15. Donskoy I. The critical conditions of filtration flow blocking in a porous channel with phase transitions // Journal of Heat and Mass Transfer Research. 2024. doi: 10.22075/JHMTR.2024.34469.1570 (in press)
  16. Gunn D.J. Diffusion and chemical reaction in catalysis and absorption // Chemical Engineering Science. 1967. V. 22. No. 11. P. 1439. doi: 10.1016/0009-2509(67)80071-X
  17. Донской И.Г. Задача Стефана в тепловыделяющем цилиндрическом образце с граничными условиями третьего рода: расчет времени расплавления // iPolytech Journal. 2024. Т. 28. № 2. С. 290. doi: 10.21285/1814-3520-2024-2-290-302
  18. Быков В.И., Цыбенова С.Б. Динамика фазовых переходов первого рода // ДАН. 2009. Т. 429. № 3. С. 347.
  19. Lutsenko N.A. Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration // Combustion Theory and Modelling. 2018. V. 22. No. 2. P. 359. doi: 10.1080/13647830.2017.1406617
  20. Crepeau J., Siahpush A.S. Solid–liquid phase change driven by internal heat generation // Comptes Rendus Mecanique. 2012. V. 340. P. 471. doi: 10.1016/j.crme.2012.03.004

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2. Fig. 1. Dependence of the position of the phase transition boundary in the heat-generating cylinder on the intensity of heat generation (Q) and the intensity of cooling (numbers next to the curves, Pe0) for Bi = 20 and κ = 1: (a) constant flow rate; (b) constant flow rate.

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