Abstract
Numerical simulation of transient melting regimes inside an enclosure in the presence of a local heat source has been carried out. Mathematical model formulated in terms of dimensionless variables such as stream function, vorticity, and temperature has been numerically solved by finite difference method. Effects of the Rayleigh number 4·105 ≤ Ra ≤ 5·107, Stefan number 2.21 ≤ Ste ≤ 5.53, and dimensionless time on velocity and temperature fields as well as on the local Nusselt number along the heat source surface have been analyzed in detail. The transient effects of the considered process at high values of the Rayleigh number have been identified.
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References
S. Raoux and M. Wutting, Phase Change Materials. Science and Applications, Springer, Berlin, 2009.
C. Gau and R. Viskanta, Melting and solidification of pure melting on a vertical wall, ASME J. Heat Transfer, 1986, Vol. 108, P. 174-181.
Z.-X. Gong and A.S. Mujumdar, Flow and heat transfer in convection-dominated melting in a rectangular cavity heated from below, Int. J. Heat Mass Transfer, 1997, Vol. 41, P. 2573-2580.
T. Kousksou, M. Mahdaoui, A. Ahmed, and A.A. Msaad, Melting over a wavy surface in a rectangular cavity heated from below, Energy, 2014, Vol. 64, P. 212-219.
H.F. Oztop, E. Abu-Nada, Y. Varol, and A. Chamkha, Natural convection in wavy enclosures with volumetric heat sources, Int. J. Thermal Sci., 2011, Vol. 50, P. 502-514.
W. Shyy and M.-H. Chen, Steady-state natural convection with phase change, Int. J. Heat Mass Transfer, 1990, Vol. 33, P. 2545-2563.
F.L. Tan and C.P. Tso, Cooling of mobile electronic devices using phase change materials, Appl. Thermal Engng, 2004, Vol. 24, P. 159-169.
S.C. Fok, W. Shen, and F.L. Tan, Cooling of portable hand-held electronic devices using phase change materials in finned heat sinks, Int. J. Thermal Sci., 2010, Vol. 49, P. 109-117.
X. Sun, Q. Zhang, M.A. Medina, and S. Liao, Performance of a free-air cooling system for telecommunications base stations using phase change materials (PCMs): in-situ tests, Applied Energy, 2015, Vol. 147, P. 325-334.
Y.-H. Wang and Y.-T. Yang, Three-dimensional transient cooling simulations of a portable electronic device using PCM (phase change materials) in multi-fin heat sink, Energy, 2011, Vol. 36, P. 5214-5224.
Y.-T. Yang and Y.-H. Wang, Numerical simulation of three-dimensional transient cooling application on a portable electronic device using phase change material, Int. J. Thermal Sci., 2012, Vol. 51, P. 155-162.
S.G. Martyushev and M.A. Sheremet, Numerical analysis of the convection-radiation heat transfer in a closed air cavity with local heat source, Komputernye issledovaniya i modelirovanie, 2014, Vol. 6, No. 3, P. 383-396.
Y. Belhamadia, A.S. Kane, and A. Fortin, An enhanced mathematical model for phase change problems with natural convection, Int. J. Numer. Anal. and Modeling, Series B, 2012, Vol. 2, P. 192-206.
V.F. Strizhov (Ed.). Numerical Investigations of Natural Convection Flows of Solidifying Liquid. Trudy IBRAE RAN (general editor L.A. Bolshov), issue 2, Nauka, Moscow, 2007.
N.S. Bondareva and M.A. Sheremet, Study of melting of a pure gallium under influence of magnetic field in a square cavity with a local heat source, IOP Conf. Series: Materials Sci. and Engng, 2015, Vol. 93, P. 012004-1-012004-6.
N.S. Bondareva and M.A. Sheremet, Numerical simulation of melting of a pure gallium in a rectangular enclosure, in: Proceedings of XII Int. Conf. of students and young scientists Prospects of Fundamental Sciences Development Tomsk Polytechn. Univ., Tomsk, 2015, P. 627-629.
S.G. Martyushev and M.A. Sheremet, Conjugate natural convection combined with surface thermal radiation in an air filled cavity with internal heat source, Int. J. Thermal Sci., 2014, Vol. 76, P. 51-67.
V.M. Paskonov, V.I. Polezhaev, and L.A. Chudov, Numerical Modeling of Heat and Mass Exchange Processes, Nauka, Moscow, 1984.
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The work has been supported financially by the Russian Foundation for Basic Research (Grant No. 14-08-31137 mol_a) and the Council for Grants of the RF President for young Russian scientists (Grant MD-6942.2015.8).
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Bondareva, N.S., Sheremet, M.A. Mathematical simulation of melting inside a square cavity with a local heat source. Thermophys. Aeromech. 23, 553–565 (2016). https://doi.org/10.1134/S0869864316040089
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DOI: https://doi.org/10.1134/S0869864316040089