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Free convection of nanofluid filled enclosure using lattice Boltzmann method (LBM)

Abstract

The lattice Boltzmann method (LBM) is used to examine free convection of nanofluids. The space between the cold outer square and heated inner circular cylinders is filled with water including various kinds of nanoparticles: TiO2, Ag, Cu, and Al2O3. The Brinkman and Maxwell-Garnetts models are used to simulate the viscosity and the effective thermal conductivity of nanofluids, respectively. Results from the performed numerical analysis show good agreement with those obtained from other numerical methods. A variety of the Rayleigh number, the nanoparticle volume fraction, and the aspect ratio are examined. According to the results, choosing copper as the nanoparticle leads to obtaining the highest enhancement for this problem. The results also indicate that the maximum value of enhancement occurs at λ = 2.5 when Ra = 106 while at λ = 1.5 for other Rayleigh numbers.

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Abbreviations

c p :

specific heat

c i :

discrete particle speeds

f :

density distribution function

f eq :

density equilibrium distribution function

g :

distribution functions for energy

g eq :

equilibrium distribution functions for energy

g neq :

non-equilibrium distribution functions for energy

g y :

gravitational acceleration (m·s−2)

k :

conductivity

\(\overline {Nu}\) :

average Nusselt number

Nu :

local Nusselt number

Pr :

Prandtl number (= ν/α)

Ra :

Rayleigh number (= ΔTH 3/(αν))

r :

radius of circle

T :

temperature

(u, v):

velocity in x- and y-directions

α :

thermal diffusivity (m2·s−1)

Θ :

dimensionless temperature

ϕ :

volume fraction

µ:

dynamic viscosity (Pa·s−1)

ν :

kinematic viscosity (m2·s−1)

λ :

aspectratio(=L/(2r))

ρ :

density(kg·m−3)

τ c :

temperature relaxation time

τ v :

flow relaxation time

β :

coefficient of thermal expansion (K−1)

δ T :

thermal boundary layer thickness

c:

cold

h:

hot

nf:

nanofluid

f:

base fluid

s:

solid particles

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Correspondence to M. Sheikholeslami.

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Sheikholeslami, M., Gorji-Bandpy, M. & Domairry, G. Free convection of nanofluid filled enclosure using lattice Boltzmann method (LBM). Appl. Math. Mech.-Engl. Ed. 34, 833–846 (2013). https://doi.org/10.1007/s10483-013-1711-9

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  • DOI: https://doi.org/10.1007/s10483-013-1711-9

Key words

  • lattice Boltzmann method (LBM)
  • nanofluid
  • natural convection
  • concentric annular cavity

Chinese Library Classification

  • O357.5+3

2010 Mathematics Subject Classification

  • 80A20