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Study of coupled double diffusive convection–radiation in a tilted cavity via a hybrid multi-relaxation time-lattice Boltzmann-finite difference and discrete ordinate methods

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Abstract

The coupled double diffusive natural convection and radiation in a tilted and differentially heated square cavity containing a non-gray air-CO2 (or air-H2O) mixtures was numerically investigated. The horizontal walls are insulated and impermeable and the vertical walls are maintained at different temperatures and concentrations. The hybrid lattice Boltzmann method with the multiple-relaxation time model is used to compute the hydrodynamics and the finite difference method to determine temperatures and concentrations. The discrete ordinates method combined to the spectral line-based weighted sum of gray gases model is used to compute the radiative term and its spectral aspect. The effects of the inclination angle on the flow, thermal and concentration fields are analyzed for both aiding and opposing cases. It was found that radiation gas modifies the structure of the velocity and thermal fields by generating inclined stratifications and promoting the instabilities in opposing flows.

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Abbreviations

a k :

Weighting factor in SLW model

C :

Molecular concentration (mol m−3)

C 0 :

Reference concentration = (Cl + Ch)/2 (mol m−3)

C abs :

Absorption cross-sections (m2 mol−1)

D :

Mass diffusivity (m2 s−1)

g :

Gravitational acceleration (m s−2)

I :

Radiation intensity (W m−2 sr−1)

I 0 :

Black body radiation intensity (Wm−2sr−1)

k :

Thermal conductivity (W m−1 K−1)

L :

Enclosure width (m)

M g :

Number of discrete directions

Le :

Lewis number α/D

\( \overrightarrow {n} \) :

Outer unit vector normal

N :

Buoyancy ratio

Nu C , R :

Averaged convective (or radiative) Nusselt number

Nu T :

Averaged total Nusselt number at the side walls

Pl :

Planck number = (k/L)/(4σ T 40 )

Pr :

Prandtl number = ν/α

q R :

Radiative heat flux (Wm−2)

Ra :

Rayleigh number = gβ(T h  − T c )L 3 /να

Sh :

Sherwood number

T :

Temperature (K)

T h , T c :

Hot and cold wall temperatures (K)

T 0 :

Average temperature = (T h  + T c )/2 (K)

u, v :

Velocity components (m s−1)

w m :

Quadrature weights

x, y :

Cartesian coordinates (m)

α :

Thermal diffusivity (m2 s−1)

β T(C) :

Thermal (mass) expansion coefficient [K−1 (m3)]

ε w :

Emissivity of radiative surface

φ :

Inclination angle

μ, η:

Direction cosines

ν:

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

κ :

Absorption coefficient (m−1)

σ :

Stefan-Boltzmann constant (W K−4 m−2)

ψ :

Stream function (m2 s)

\( \overrightarrow {\Gamma } \) :

Direction vector

\( \overrightarrow {\nabla } \) :

Gradient operator

c, h, (l, h):

Cold, hot, (concentration: low, high)

f :

Fluid

m :

Index for discrete direction in the DOM

R :

Radiative quantity

s :

Solid

T :

Total conductive and radiative quantity

w :

Wall

0 :

Reference state

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Acknowledgments

The authors are very grateful to Dr. D. Lemonnier (Director of Research at CNRS, Institut Pprime, CNRS-ENSMA-University of Poitiers, France) for kindly providing us the subroutines (DOM & SLW) for computations of the radiation. In addition, the authors thank the reviewers for the thorough reading of the manuscript and for their valuable comments, which led to significant improvements in this paper.

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Authors and Affiliations

  1. Laboratoire de Mécanique & Energétique, Faculté des Sciences, Université Mohammed Premier, 60000, Oujda, Morocco

    Fayçal Moufekkir, Mohammed Amine Moussaoui & Ahmed Mezrhab

  2. Laboratoire Génie Civil & Géo-Environnement (LGCgE), University of Lille Nord de France, 59000, Lille, France

    Hassan Naji

  3. University of Artois, LGCgE, Technoparc Futura, 62400, Béthune, France

    Hassan Naji

Authors
  1. Fayçal Moufekkir
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  2. Mohammed Amine Moussaoui
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  3. Ahmed Mezrhab
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  4. Hassan Naji
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Correspondence to Ahmed Mezrhab.

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Moufekkir, F., Moussaoui, M.A., Mezrhab, A. et al. Study of coupled double diffusive convection–radiation in a tilted cavity via a hybrid multi-relaxation time-lattice Boltzmann-finite difference and discrete ordinate methods. Heat Mass Transfer 51, 567–586 (2015). https://doi.org/10.1007/s00231-014-1423-0

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  • DOI: https://doi.org/10.1007/s00231-014-1423-0

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