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Lattice Boltzmann simulation of natural convection in nanofluid-filled 2D long enclosures at presence of magnetic field

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Abstract

In this paper, the effects of a magnetic field on natural convection flow in filled long enclosures with Cu/water nanofluid have been analyzed by lattice Boltzmann method. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 103–105, the volumetric fraction of nanoparticles between 0 and 6 %, the aspect ratio of the enclosure between A = 0.5 and 2. The Hartmann number has been varied from Ha = 0 to 90 with interval 30 while the magnetic field is considered at inclination angles of θ = 0°, 30°, 60° and 90°. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers and the aspect ratios. Heat transfer decreases with the growth of the aspect ratio but this growth causes the effect of the nanoparticles to increase. The magnetic field augments the effect of the nanoparticles at high Rayleigh numbers (Ra = 105). The effect of the nanoparticles rises for high Hartmann numbers when the aspect ratio increases. The rise in the magnetic field inclination improves heat transfer at aspect ratio of A = 0.5.

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Abbreviations

B :

Magnetic field

c :

Lattice speed

c i :

Discrete particle speeds

c p :

Specific heat at constant pressure

F :

External forces

f :

Density distribution functions

f eq :

Equilibrium density distribution functions

g :

Internal energy distribution functions

g eq :

Equilibrium internal energy distribution functions

g y :

Gravity

Gr:

Grashof number \({\left({{Gr}}=\frac{\beta g_y H^{3}(T_H-T_C)}{\nu ^{2}}\right)}\)

Ha:

Hartmann number \({{{Ha}}^{2}=\frac{B^{2}L^{2}\sigma _e}{\mu}}\)

M :

Lattice number

Ma:

Mach number

Nu:

Nusselt number

Pr:

Prandtl number

R :

Constant of the gases

Ra:

Rayleigh number \({\left({{{Ra}}=\frac{\beta g_yH^{3}(T_H -T_C )}{\nu \alpha}}\right)}\)

T :

Temperature

x,y :

Cartesian coordinates

u :

Magnitude velocity

σ :

Electrical conductivity

ω i :

Weighted factor indirection i

β :

Thermal expansion coefficient

τ c :

Relaxation time for temperature

τ v :

Relaxation time for flow

ν :

Kinematic viscosity

Δx :

Lattice spacing

Δt :

Time increment

α :

Thermal diffusivity

φ :

Volume fraction

μ :

Dynamic viscosity

ψ :

Stream function value

θy:

Inclination angle

avg:

Average

C :

Cold

H :

Hot

f :

Fluid

nf:

Nanofluid

s :

Solid

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Authors and Affiliations

  1. Young Researchers Club, South Tehran Branch, Islamic Azad University, Tehran, Iran

    GH. R. Kefayati

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  1. GH. R. Kefayati
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Correspondence to GH. R. Kefayati.

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Communicated by O. Zikanov.

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Kefayati, G.R. Lattice Boltzmann simulation of natural convection in nanofluid-filled 2D long enclosures at presence of magnetic field. Theor. Comput. Fluid Dyn. 27, 865–883 (2013). https://doi.org/10.1007/s00162-012-0290-x

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