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Penetrative convection of water in cavities cooled from below. (English) Zbl 1390.76834
Summary: Transient natural convection in water-filled square enclosures with the bottom wall cooled at \(0^\circ C\), and the top wall heated at a temperature spanning from 8 to \(80^\circ C\), is studied numerically for different widths of the cavity in the hypothesis of temperature-dependent physical properties, starting from the initial condition of motionless fluid at the uniform temperature of the top wall. The sidewalls are assumed to be adiabatic. A computational code based on the SIMPLE-C algorithm is used to solve the system of the mass, momentum and energy transfer governing equations. The propagation of convective motion from the bottom toward the top of the enclosure is investigated up to the achievement of a steady-state or a periodically-oscillating asymptotic solution. It is found that the ratio between the penetration depth and the cavity size increases as the temperature of the heated top wall decreases and the cavity size increases. Moreover, when the configuration is such that the buoyancy force in the water layer confined between the cooled bottom wall and the density-inversion isotherm is of the order of that required for the onset of convection, the asymptotic solution is periodical. Finally, the coefficient of convection decreases with increasing both the cavity width and the imposed temperature difference. Dimensionless correlations are developed for the calculation of the heat transfer rate across the enclosure and the penetration depth.
MSC:
76R10 Free convection
76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
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[1] Veronis, G., Penetrative convection, Astrophys J, 137, 641-663, (1963) · Zbl 0123.46103
[2] Musman, S., Penetrative convection, J Fluid Mech, 31, 343-360, (1968)
[3] Moore, D. R.; Weiss, N. O., Nonlinear penetrative convection, J Fluid Mech, 61, 553-581, (1973)
[4] Kuznetsova, D. V.; Sibgatullin, I. N., Transitional regimes of penetrative convection in a plane layer, Fluid Dyn Res, 44, (2012) · Zbl 1309.76188
[5] Blake, K. R.; Poulikakos, D.; Bejan, A., Natural convection near 4 °C in a horizontal water layer heated from below, Phys Fluids, 27, 2608-2616, (1984) · Zbl 0548.76069
[6] Tong, W.; Koster, J. N., Penetrative convection in sublayer of water including density inversion, Wärme und Stoffübertragung, 29, 37-49, (1993)
[7] Townsend, A. A., Natural convection in water over an ice surface, Quart J Roy Metereol Soc, 90, 248-259, (1964)
[8] Zubkov, P. T.; Kalabin, E. V., Numerical investigation of the natural convection of water in the neighborhood of the density inversion point for grashof numbers up to 10^6, Fluid Dyn, 36, 944-951, (2001) · Zbl 1175.76055
[9] Zubkov, P. T.; Kalabin, E. V.; Yakovlev, A. V., Investigation of natural convection in a cubic cavity near 4 °C, Fluid Dyn, 37, 847-853, (2002) · Zbl 1161.76432
[10] Li, Y. R.; Ouyang, Y. Q.; Hu, Y. P., Pattern formation of Rayleigh-Bénard convection of cold water near its density maximum in a vertical cylindrical container, Phys Rev E, 86, (2012)
[11] Li, Y. R.; Yuan, X. F.; Wu, C. M.; Hu, Y. P., Natural convection of water near its density maximum between horizontal cylinders, Int J Heat Mass Transf, 54, 2550-2559, (2011) · Zbl 1217.80062
[12] Yuan, X. F.; Li, Y. R., Natural convective heat transfer of water near its density maximum in an eccentric horizontal annulus, Int J Thermal Sci, 60, 85-93, (2012)
[13] Li, Y. R.; Hu, Y. P.; Yuan, X. F., Natural convection of water near its density maximum around a cylinder inside an elliptical enclosure along slender orientation, Numer Heat Transf A, 62, 780-797, (2012)
[14] Li, Y. R.; Hu, Y. P.; Yuan, X. F., Three-dimensional numerical simulation of natural convection of water near its density maximum in a horizontal annulus, Int J Thermal Sci, 71, 274-282, (2013)
[15] Hu, Y. P.; Li, Y. R.; Yuan, X. F.; Wu, C. M., Natural convection of cold water near its density maximum in an elliptical enclosure containing a coaxial cylinder, Int J Heat Mass Transf, 60, 170-179, (2013)
[16] Hu, Y. P.; Li, Y. R.; Wu, C. M., Comparison investigation on natural convection of cold water near its density maximum in annular enclosures with complex configurations, Int J Heat Mass Transf, 72, 572-584, (2014)
[17] Forbes, R. E.; Cooper, J. W., Natural convection in a horizontal layer of water cooled from above to near freezing, J Heat Transf − Trans ASME, 97, 47-53, (1975)
[18] Vasseur, P.; Robillard, L., Transient natural convection heat transfer in a mass of water cooled through 4 °C, Int J Heat Mass Transf, 23, 1195-1205, (1980) · Zbl 0433.76070
[19] Alawadhi, E. M., Cooling process of water in a horizontal circular enclosure subjected to non-uniform boundary conditions, Energy, 36, 586-594, (2011)
[20] P.J. Linstrom, W.G. Mallard, Eds., NIST Chemistry WebBook, NIST standard reference database number 69, National Institute of Standards and Technology, Gaithersburg MD, 20899, USA, http://webbook.nist.gov (last accessed date 25th July 2014).
[21] Gebhart, B.; Mollendorf, J. C., A new density relation for pure and saline water, Deep-Sea Res, 24, 831-848, (1977)
[22] Ishikawa, M.; Hirata, T.; Noda, S., Numerical simulation of natural convection with density inversion in a square cavity, Numer Heat Transf A, 37, 395-406, (2000)
[23] Van Doormaal, J. P.; Raithby, G. D., Enhancements of the simple method for predicting incompressible fluid flows, Numer Heat Transfer, 7, 147-163, (1984) · Zbl 0553.76005
[24] Patankar, S. V.; Spalding, D. B., A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, Int J Heat Mass Transf, 15, 1787-1797, (1972) · Zbl 0246.76080
[25] Patankar, S. V., Numerical heat transfer and fluid flow, (1980), Hemisphere Publ. Co. Washington, DC · Zbl 0595.76001
[26] Leonard, B. P., A stable and accurate convective modelling procedure based on quadratic upstream interpolation, Comput Methods Appl Mech Eng, 19, 59-78, (1979) · Zbl 0423.76070
[27] de Vahl Davis, G., Natural convection of air in a square cavity: a bench mark numerical solution, Int J Numer Methods Fluids, 3, 249-264, (1983) · Zbl 0538.76075
[28] Mahdi, H. S.; Kinney, R. B., Time-dependent natural convection in a square cavity: application of a new finite volume method, Int J Numer Methods Fluids, 11, 57-86, (1990) · Zbl 0697.76097
[29] Hortmann, M.; Peric, M.; Scheuerer, G., Finite volume multigrid prediction of laminar natural convection: bench-mark solutions, Int J Numer Methods Fluids, 11, 189-207, (1990) · Zbl 0711.76072
[30] Wan, D. C.; Patnaik, B. S.V.; Wei, G. W., A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution, Numer Heat Transf, 40, 199-228, (2001)
[31] Bejan, A., Convection heat transfer, (2004), John Wiley & Sons, Inc Hoboken, New Jersey
[32] Incropera, F. P.; Dewitt, D. P.; Bergman, T. L.; Lavine, A. S., Fundamentals of heat and mass transfer, (2007), John Wiley & Sons, Inc Hoboken, New Jersey
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