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Research Papers: Natural and Mixed Convection

Effects of Thermophysical Variable Properties on Liquid-Sodium Convective Flows in a Square Enclosure

[+] Author and Article Information
Blas Zamora

Department of Thermal and Fluids Engineering,
Technical University of Cartagena,
Doctor Fleming s/n,
Cartagena 30202, Spain
e-mail: blas.zamora@upct.es

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 30, 2018; final manuscript received December 21, 2018; published online February 4, 2019. Assoc. Editor: Srinath V. Ekkad.

J. Heat Transfer 141(3), 032501 (Feb 04, 2019) (11 pages) Paper No: HT-18-1565; doi: 10.1115/1.4042490 History: Received August 30, 2018; Revised December 21, 2018

The influence of the variable properties on the buoyancy-driven flows of liquid sodium established in a square enclosure including two inner heated plates is numerically investigated. Two-dimensional turbulent simulations are obtained, considering uniform wall temperature heating conditions. The low-Reynolds k–ω turbulence model is employed. The average Nusselt number and the dimensionless mass-flow rate evaluated between the inner plates are obtained for a wide range of the Rayleigh number, varying from 103 to 1012. Several practical correlations are presented. The results obtained for different heating intensities are analyzed and compared. The expected decay in the heat transfer coefficients is less relevant than that previously obtained for airflows. The thermal structure of the flow into the enclosure is also shown.

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References

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Figures

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Fig. 1

Problem statement: (a) configuration of simple vertical channel, considered for validation purposes, (b) configuration of enclosure, also considered for validation purposes, (c) configuration of enclosure with two internal, centered, heated plates, considered in most of the presented results, and (d) typical employed mesh

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Fig. 2

Evolution of the main thermophysical properties of liquid sodium, as a function of temperature: (a) heat capacity and thermal conductivity and (b) density and kinematic viscosity

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Fig. 3

Validation of the numerical simulation. Configuration of simple channel, Fig. 1(a). Comparison with asymptotes of Elenbaas [23] and Churchill and Chu [22].

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Fig. 4

Validation of the numerical simulation. Enclosure configuration, Figs. 1(b): (a) differentially heated by the sides; comparison with Mohamad and Viskanta [24] and Sudha and Velusamy [3] and (b) heated from below; comparison with Rossby, referred by Kek and Muller [25] and Sudha and Velusamy [3].

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Fig. 5

Dimensionless mass-flow rate through the channel and average Nusselt numbers at thermally active walls of enclosure given in Fig. 1(c), as a function of Rayleigh number RaHc. Heating parameter Λ = 0.01.

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Fig. 6

Dimensionless mass-flow rate through the channel and average Nusselt numbers at thermally active walls of enclosure given in Fig. 1(c), as a function of Rayleigh number RaHc and heating parameter Λ: (a) Λ = 0.5 and (b) Λ = 3

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Fig. 7

Average Nusselt number at the internal side of the inner plate of enclosure given in Fig. 1(c), as a function of Rayleigh number RaHc and values of heating parameter 0.1 ≤ Λ ≤ 3: (a) 103 ≤ RaHc ≤ 108 and (b) 108 ≤ RaHc ≤ 1012

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Fig. 8

Ratio NuHc,in/NuHc,in,B, as a function of Λ and the Rayleigh number RaHc: (a) 103 ≤ RaHc ≤ 108 and (b) 108 ≤ RaHc ≤ 1012. Configuration given in Fig. 1(c).

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Fig. 9

Fitting constant K for correlations given by Eq. (22), as a function of Rayleigh number RaHc. Configuration of enclosure given in Fig. 1(c).

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Fig. 10

Isotherms for configuration of Fig. 1(c), for Λ = 0.01 and different values of Rayleigh number: (a) RaHc = 105, (b) RaHc = 107, (c) RaHc = 109, and (d) RaHc = 1011. Representative values of θ = (T − T)/ΛT have been included.

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Fig. 11

Isotherms for configuration of Fig. 1(c), for RaHc = 109 and different values of heating parameter Λ: (a) Λ = 0.01, (b) Λ = 0.5, (c) Λ = 1, and (d) Λ = 3. Representative values of θ = (T − T)/ΛT have been included.

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Fig. 12

Computed turbulent quantities: (a) dimensionless turbulent kinetic energy and (b) dimensionless turbulent kinematic viscosity. Configuration of Fig. 1(c), for RaHc = 109 and Λ = 0.01. Representative values of k/[RaHc(ν/Hc)2] and νt/ν, respectively, have been included.

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