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Natural Convection Heat Transfer of a Nanofluid into a Cubical Enclosure: Lattice Boltzmann Investigation

  • Research Article - Mechanical Engineering
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Abstract

Through this paper, the hydrodynamic and thermal characteristics of Ag–water nanofluid, filling a differentially heated cubic enclosure, are numerically investigated. To do so, a developed computer code based on the lattice Boltzmann approach coupled with the finite-difference method is used. The later has been validated after comparison between the obtained results and experimental and numerical ones already found in the literature. To make clear the effect of main parameters such as the Rayleigh number, the nanoparticle volume fraction, and the enclosure inclination angle, the convection phenomenon was reported by means of streamlines, temperature iso-surfaces, and velocity and temperature profiles. A special attention was paid to the Nusselt number evolution. Compared to a 2D investigation, and when the convection mode dominates, taking into account the third direction leads to significant modifications on the nanofluid motion and heat transfer as well. As the conductive regime dominates, the use of a 2D configuration is found to be valid to predict the studied phenomenon. It is to note that the three-dimensional D3Q19 model was adopted based on a cubic lattice, where each pattern of the later is characterized by 19 discrete speeds.

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Abbreviations

\({a}\) :

Coefficient in external forces (\({= g \,\beta)}\)

\({a_{ij}}\) :

Coefficients in equation (13)

\({c}\) :

Cold

\({c_{s}}\) :

Sound velocity in the lattice (\({c_{s}=1/\sqrt{3})}\)

\({C_{p}}\) :

Specific heat at constant pressure, (J kg\({^{-1}}\)  K\({^{-1})}\)

\({f}\) :

fluid

\({f_{{\rm eq}}}\) :

Equilibrium distribution function

\({F_{{\rm ext}}}\) :

External force

\({f_{i}}\) :

Distribution function

\({h}\) :

Hot

\({k}\) :

Thermal conductivity, (W m\({^{-1}}\)  K\({^{-1})}\)

\({H_{ x,y,z}}\) :

Enclosure dimensions, (m)

\({m_{j}}\) :

Moments

nf:

Nanofluid

Nu:

Mean Nusselt number

Pr:

Prandtl number (Pr = \({v/\alpha)}\)

\({s}\) :

Solid particles

\({S_{j}}\) :

Relaxation rate

\({t}\) :

Time, (s)

\({T}\) :

Temperature, (K)

\({T_{0}}\) :

Mean temperature, (\({= (T_{{\rm h}}}\) + \({T_{{\rm c}})}\) / 2)

Ra:

Rayleigh number, (= 2\({T_{0}}\) H\({^{3}}\) a/ \({\nu}\) k)

\({u}\) :

Horizontal velocity component, (m)

\({v}\) :

Vertical velocity component, (m)

\({w}\) :

Depth velocity component, (m)

\({x, y, z}\) :

Dimensional cartesian coordinates, (m)

\({X,Y,Z}\) :

Dimensionless coordinates, (\({X = x/H}\) , \({Y = y/H}\) , \({Z = z/H}\))

\({\alpha}\) :

Thermal diffusivity, (m\({^{2}}\)  s\({^{-1})}\)

\({\beta}\) :

Thermal expansion coefficient, (K\({^{-1})}\)

\({\theta}\) :

Dimensionless temperature

\({\omega_{i}}\) :

Coefficients of the equilibrium function

\({\rho}\) :

Density, (kg m\({^{-3})}\)

\({\phi}\) :

Nanoparticles volume fraction

\({\varepsilon}\) :

Energy square

\({\nu}\) :

Kinematic viscosity, m\({^{2}}\)  s\({^{-1}}\)

\({\Omega }\) :

Collision operator

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Authors and Affiliations

  1. Laboratory of Transport Phenomena, USTHB, Algiers, 16111, Algeria

    Abdelkader Boutra, Karim Ragui, Nabila Labsi & Youb Khaled Benkahla

  2. Preparatory School of Science and Technology, Algiers, 16111, Algeria

    Abdelkader Boutra

  3. LMT - ENS Cachan - CNRS - Paris Saclay University, 94230, Cachan, France

    Rachid Bennacer

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  1. Abdelkader Boutra
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Correspondence to Abdelkader Boutra.

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Boutra, A., Ragui, K., Labsi, N. et al. Natural Convection Heat Transfer of a Nanofluid into a Cubical Enclosure: Lattice Boltzmann Investigation. Arab J Sci Eng 41, 1969–1980 (2016). https://doi.org/10.1007/s13369-016-2052-3

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