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Research Papers: SPECIAL SECTION PAPERS

Three-Dimensional Steady and Oscillatory Natural Convection in a Rectangular Enclosure With Heat Sources

[+] Author and Article Information
Amin Bouraoui

LEAP Laboratory,
Department of Mechanical Engineering,
Faculty of Sciences Technology,
University Constantine 1,
Route de Ain El. Bey,
Constantine 25000, Algeria
e-mail: br.amin@yahoo.fr

Rachid Bessaïh

Professor
LEAP Laboratory,
Department of Mechanical Engineering,
Faculty of Sciences Technology,
University Constantine 1,
Route de Ain El. Bey,
Constantine 25000, Algeria
e-mail: bessaih.rachid@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received September 8, 2014; final manuscript received January 30, 2015; published online June 1, 2016. Assoc. Editor: Ziad Saghir.

J. Heat Transfer 138(9), 091001 (Jun 01, 2016) (8 pages) Paper No: HT-14-1594; doi: 10.1115/1.4032949 History: Received September 08, 2014; Revised January 30, 2015

In this paper, a numerical study of three-dimensional (3D) natural convection air-cooling of two identical heat sources, simulating electronic components, mounted in a rectangular enclosure was carried out. The governing equations were solved by using the finite-volume method based on the SIMPLER algorithm. The effects of Rayleigh number Ra, spacing between heat sources d, and aspect ratios Ax in x-direction (horizontal) and Az in z-direction (transversal) of the enclosure on heat transfer were investigated. In steady state, when d is increased, the heat transfer is more important than when the aspect ratios Ax and Az are reduced. In oscillatory state, the critical Rayleigh numbers Racr for different values of spacing between heat sources and their aspect ratios, at which the flow becomes time dependent, were obtained. Results show a strong relation between heat transfers, buoyant flow, and boundary layer. In addition, the heat transfer is more important at the edge of each face of heat sources than at the center region.

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References

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Figures

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Fig. 1

(a) The 3D system scheme of a rectangular enclosure, which contains two identical heated sources and (b) diagram of all faces of two heat sources

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Fig. 2

Comparison between our numerical results and those of Sezai and Mohamad [6] of the local Nusselt number Nu for Ra = 103 and 104

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Fig. 3

Average Nusselt number in each face of heat sources (Nuavg) for different spacing and three Rayleigh numbers: (a) Ra = 103, (b) Ra = 104, and (c) Ra = 105

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Fig. 4

Average Nusselt number in each face of heat sources (Nuavg) for different aspect ratios Ax at Ra = 105

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Fig. 5

Average Nusselt number in each face of heat sources (Nuavg) for different aspect ratios Az at Ra = 105

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Fig. 6

Variation of overall Nusselt number with time and for different spacing between the heat sources 2 × d, d, and 3/4 × d at critical states and two dimensionless time step Δτ

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Fig. 7

Time history of the overall average heat transfer at critical Rayleigh numbers for different aspect ratios: Ax = l/H = 0.635, (5/4) × Ax, and (7/4) × Ax. The points (a), (b), (c), (d), (e), and (f) correspond to dimensionless times τa=1.652, τb=1.658, τc=1.661, τd=1.669, τe=1.675, and τf=1.678, respectively.

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Fig. 8

Time history of local Nusselt number at face East1 for various dimensionless times at critical Rayleigh number Racr = 1.2 × 106 and aspect ratio (5/4) × Ax: (a) τa=1.652, (b) τb=1.658, (c) τc=1.661, (d) τd=1.669, (e) τe=1.675, and (f) τf=1.678

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Fig. 9

Velocity vector U–V in the x–y plane at z = 2 at Racr = 1.2 × 106 and aspect ratio (5/4) × Ax

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Fig. 10

Power spectrum energy with frequency at Racr = 2.2 × 105 and 5/2 × (ws/H)

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Fig. 11

Amplitude in each face of heat sources for different spacing at critical Rayleigh numbers

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Fig. 12

Amplitude in each face of heat sources for different aspect ratios Az at critical Rayleigh numbers

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