Theoretical and Computational Fluid Dynamics

, Volume 27, Issue 6, pp 865–883 | Cite as

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

Original Article

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.

Keywords

Natural convection Long enclosures Nanofluid Magnetic field Lattice Boltzmann method 

List of symbols

B

Magnetic field

c

Lattice speed

ci

Discrete particle speeds

cp

Specific heat at constant pressure

F

External forces

f

Density distribution functions

feq

Equilibrium density distribution functions

g

Internal energy distribution functions

geq

Equilibrium internal energy distribution functions

gy

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

Greek letters

σ

Electrical conductivity

ωi

Weighted factor indirection i

β

Thermal expansion coefficient

τc

Relaxation time for temperature

τv

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

Subscripts

avg

Average

C

Cold

H

Hot

f

Fluid

nf

Nanofluid

s

Solid

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Young Researchers Club, South Tehran BranchIslamic Azad UniversityTehranIran

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