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Research Papers: Natural and Mixed Convection

Lattice Boltzmann Modeling of Natural Convection in a Large-Scale Cavity Heated From Below by a Centered Source

[+] Author and Article Information
Noureddine Abouricha

LPMMAT,
Department of Physics,
Faculty of Sciences Aïn Chock,
Hassan II University of Casablanca,
Casablanca 20100, Morocco
e-mail: abouricha.noureddine@gmail.com

Mustapha El Alami

LPMMAT,
Department of Physics,
Faculty of Sciences Aïn Chock,
Hassan II University of Casablanca,
Casablanca 20100, Morocco
e-mails: mustapha.elalami@univh2c.ma;
elalamimus@gmail.com

Ayoub Gounni

LPMMAT,
Department of Physics,
Faculty of Sciences Aïn Chock,
Hassan II University of Casablanca,
Casablanca 20100, Morocco
e-mail: gounni.ayoub@gmail.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 17, 2018; final manuscript received February 11, 2019; published online April 17, 2019. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 141(6), 062501 (Apr 17, 2019) (9 pages) Paper No: HT-18-1095; doi: 10.1115/1.4042905 History: Received February 17, 2018; Revised February 11, 2019

Turbulent natural convection in a large-scale cavity has taken a great attention thanks to its importance in many engineering applications such as building. In this work, the lattice Boltzmann method (LBM) is used to simulate turbulent natural convection heat transfer in a small room of housing heated from below by means of a heated floor. The ceiling and the four vertical walls of the room are adiabatic except for a portion of one vertical wall. This portion simulates a glass door with a cold temperature θc = 0. The cavity is filled by air (Pr = 0.71) and heated from below with uniformly imposed temperature θh = 1. The effects of the heat source length (Lr) and Rayleigh number (Ra) on the flow structure and heat transfer are studied for ranges of 0.2 ≤ Lr ≤ 0.8 and 5 × 106 ≤Ra ≤ 108. The heat transfer is examined in terms of local and mean Nusselt numbers. The results show that an increase in Rayleigh number or in heat source length increases the temperature in the core of the cavity. The flow structure shows that turbulent natural convection regime is fully developed for Ra = 108. Correlations for mean Nusselt number as a function with Ra for different values of Lr are expressly derived.

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References

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Figures

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Fig. 1

Physical problem (small room of housing)

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Fig. 2

Lattice and D2Q9 model

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Fig. 3

Time evolutions of average Nusselt number (0.2 ≤ Lr ≤ 0.8) and stream function at the center (Lr = 0.8) for Ra = 108

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Fig. 4

Isotherms (left) and streamlines (right) for Ra = 108 and for different values of Lr: (a) Lr = 0.2, (b) Lr = 0.4, (c) Lr = 0.6, and (d) Lr = 0.8

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Fig. 5

Dimensionless horizontal velocity profiles U (0.5,y) along the vertical centerline for Ra = 108 and for different values of Lr

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Fig. 6

Dimensionless vertical velocity profiles V(x,0.5) along the horizontal centerline for Ra = 108 and for different values of Lr

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Fig. 7

Temperature profiles along the horizontal centerline for Ra = 108 and for different values of Lr

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Fig. 8

Temperature profiles along the vertical centerline for Ra = 108 and for different values of Lr

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Fig. 9

Variation of the temperature at the center θ (0.5,0.5) with heat source length Lr for Ra = 108

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Fig. 10

Local Nusselt number variation with y along the cold wall for Ra = 108 and for different values of Lr

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Fig. 11

Local Nusselt number variation with x along the horizontal wall, for Ra = 108 and for different values of Lr

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Fig. 12

Average Nusselt number variation with heat source length Lr for various Ra

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Fig. 13

Average Nusselt number variation with Rayleigh number for various Lr

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