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Research Papers: Radiative Heat Transfer

Investigation of Double Diffusive Natural Convection in Presence of Gray Gas Radiation Within a Square Cavity Using Multiple Relaxation Time Lattice Boltzmann Method

[+] Author and Article Information
A. Mezrhab

e-mail: amezrhab@yahoo.fr
Laboratoire de Mécanique & Energétique,
Faculté des sciences,
Université Mohammed Premier,
Oujda 60000, Morocco

J. P. Fontaine

Université Blaise Pascal,
Institut Pascal–GePEB axis,
UMR 6602, BP10488, F-63000,
Clermont Ferrand, France

M. Bouzidi

Université Blaise Pascal,
Institut Pascal axe MMS,
UMR 6602, IUT d'Aillier,
B.P. 2235, Avenue Aristide Briand,
Montluçon cedex 03101, France

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received July 2, 2012; final manuscript received May 2, 2013; published online August 19, 2013. Assoc. Editor: Joon Sik Lee.

J. Heat Transfer 135(10), 102701 (Aug 19, 2013) (10 pages) Paper No: HT-12-1345; doi: 10.1115/1.4024553 History: Received July 02, 2012; Revised May 02, 2013

The present work proposes a coupling between the hybrid lattice Boltzmann, the finite difference method, and the discrete ordinates method to simulate combined double diffusive convection and volumetric radiation in a square cavity filled with an emitting and absorbing gray gas. The vertical walls are kept at different temperatures and pollutant concentrations, while the horizontal walls are insulated and impermeable. A parametric study is carried out to evaluate the influence of control parameters such as the Lewis number (Le), Planck number (Pl), and reference temperature ratio (Θ0) on the flow field as well as on heat and mass transfer. The results are presented in terms of isotherms, streamlines, isoconcentrations, average Nusselt, and Sherwood numbers. They show that the volumetric radiation accelerates the flow and significantly alters the structure of the dynamic, concentration, and temperature fields, especially when the thermal forces are dominant. On the other hand, when the mass forces are dominant, the flow is slowed down. The influence of radiation is greater on the thermal field than on the dynamic and concentration fields.

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References

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Rafieivand, M., 1999, “Etude numérique de la convection de double diffusion en présence de rayonnement en cavité rectangulaire,” Thèse de Doctorat, Université de Poitiers, Poitiers, France.
Mezrhab, A., Lemonnier, D., Meftah, S., and Benbrik, A., 2008, “Numerical Study of Double Diffusion Convection Coupled to Radiation in a Square Cavity Filled With a Participating Grey Gas,” J. Phys. D: Appl. Phys., 41, p. 195501. [CrossRef]
Lallemand, P., and Luo, L. S., 2000, “Theory of the Lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance and Stability,” Phys. Rev. E, 61, pp. 6546–6562. [CrossRef]
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Figures

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Fig. 1

Geometry of the problem: (a) cooperating flow and (b) opposite flow

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Fig. 2

Bounce-back boundary condition, xf: last fluid node, xw: physical wall, and xs: first solid node

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Fig. 3

Isolines for (a) N = 1, (b) N = −1 and at Ra = 5 × 106, Pr = 0.71, Pl = 0.02, Θ0= 1.5, and τ0 = 5

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Fig. 4

(a) Temperatures, (b) concentration, (c) and (d) horizontal and vertical velocities, respectively, at active wall for N = 1 and −1, Ra = 5 × 106, Pr = 0.71, Pl = 0.02, Θ0= 1.5, τ0=5, and Le = 0.1–10

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Fig. 5

Average Nusselt and Sherwood numbers versus Le at Pr = 0.71, Pl = 0.02, Θ0= 1.5, and for N = 2 (a) and (b) and N = −2 (c) and (d)

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Fig. 6

Isolines for (a) N = 2, (b) N = −2 and at Ra = 5 × 106 Pr = 0.71, Le = 1, Θ0 = 1.5, and τ0 =2

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Fig. 7

(a) temperatures, (b) concentration, (c) and (d) horizontal and vertical velocities, respectively, at active wall for N = 2 and −2, Ra = 5 × 106, Pr = 0.71, Le = 1, Θ0 = 1.5, τ0 = 2, and Pl = 0.0005–100

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Fig. 8

Average Nusselt and Sherwood numbers versus Pl for N = 2 (a) and (b) and N = −2 (c) and (d) at Ra = 5 × 106, Pr = 0.71, Le = 1, and Θ0 =1.5

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Fig. 9

Isolines for (a) N = 2, (b) N = −2 and at Pr = 0.71, Le = 1, Pl = 0.02, and τ0 = 2

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Fig. 10

(a) temperature, (b) concentration, (c) and (d) horizontal and vertical velocities, respectively, at active wall for N = 2 and −2, Ra = 5 × 106, τ0 = 2, Pr = 0.71, Le = 1, Pl = 0.02, and Θ0 = 0.75–10

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Fig. 11

Average Nusselt and Sherwood numbers versus Θ0 for N = 2 (a) and (b) and N = −2 (c) and (d) at Ra = 5 × 106, Pr = 0.71, Le = 1, and Pl = 0.02

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