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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 71, 2017 - Issue 2
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Original Articles

Rayleigh–Benard convection in water-based alumina nanofluid: A numerical study

, &
Pages 202-214 | Received 21 Jun 2016, Accepted 12 Oct 2016, Published online: 05 Jan 2017
 

ABSTRACT

Rayleigh–Benard (R-B) convection in water-based alumina (Al2O3) nanofluid is analyzed based on a single-component non-homogeneous volume fraction model (SCNHM) using the lattice Boltzmann method (LBM). The present model accounts for the slip mechanisms such as Brownian and thermophoresis between the nanoparticle and the base fluid. The average Nusselt number at the bottom wall for pure water is compared to the previous numerical data for natural convection in a cavity and a good agreement is obtained. The parameters considered in this study include the Rayleigh number of the nanofluid, the volume fraction of alumina nanoparticle and the aspect ratio of the cavity. For the Al2O3/water nanofluid, it is found that heat transfer rate decreases with an increase of the volume fraction of the nanoparticle. The results are demonstrated and explained with average Nusselt number, isotherms, streamlines, heat lines, and nanoparticle distribution. The effect of nanoparticles on the onset of instability in R-B convection is also analyzed.

Nomenclature

A=

aspect ratio

Cp=

specific heat, (J/kgK)

DB=

Brownian diffusion coefficient, (m2/s)

DT=

thermophoretic diffusion coefficient, (m2/s)

F=

force, (N)

H=

height, (m)

KB=

Boltzmann constant, = 1.308 × 10−231/K

Le=

Lewis number,

Nu=

Nusselt number

P=

pressure, (Pa)

Pr=

Prandtl number,

Ra=

Rayleigh number,

Re=

Reynolds number

S=

source term

Sc=

Schmidt number,

T=

temperature, (K)

W=

width, (m)

Wi=

weighing factor

d=

diameter, (nm)

ei=

discrete velocity

fi=

density distribution

g=

acceleration due to gravity, (m/s2)

gi=

temperature distribution

hi=

concentration distribution

j=

flux

k=

thermal conductivity, (W/mK)

l=

mean free path of fluid particles, = 0.17(nm)

t=

time, (s)

u=

horizontal velocity, (m/s)

v=

vertical velocity, (m/s)

x&y=

cartesian coordinates, (m)

ρ=

density, (kg/m3)

μ=

dynamic viscosity, (kg/ms)

ν=

kinematic viscosity, (m2/s)

α=

thermal diffusivity, (m2/s)

β=

thermal expansion coefficient, (1/K)

τ=

lattice relaxation time

ϕ=

nanoparticle volume fraction, (%)

Π=

heat function

T=

temperature gradient, (K/m)

ϕ=

concentration gradient, (% /m)

θ=

non-dimensional temperature

ΔT=

temperature difference, = (Th − Tc)(K)

Δt=

lattice time step

Subscripts=
T=

temperature

avg=

average

bf=

basefluid

c=

cold

conc=

concentration

h=

hot

i=

discrete lattice direction

lbm=

lattice scale

loc=

local

mom=

momentum

nf=

nanofluid

p=

particle

ref=

reference

temp=

temperature

Superscripts=
eq=

equilibrium

t=

transpose

Nomenclature

A=

aspect ratio

Cp=

specific heat, (J/kgK)

DB=

Brownian diffusion coefficient, (m2/s)

DT=

thermophoretic diffusion coefficient, (m2/s)

F=

force, (N)

H=

height, (m)

KB=

Boltzmann constant, = 1.308 × 10−231/K

Le=

Lewis number,

Nu=

Nusselt number

P=

pressure, (Pa)

Pr=

Prandtl number,

Ra=

Rayleigh number,

Re=

Reynolds number

S=

source term

Sc=

Schmidt number,

T=

temperature, (K)

W=

width, (m)

Wi=

weighing factor

d=

diameter, (nm)

ei=

discrete velocity

fi=

density distribution

g=

acceleration due to gravity, (m/s2)

gi=

temperature distribution

hi=

concentration distribution

j=

flux

k=

thermal conductivity, (W/mK)

l=

mean free path of fluid particles, = 0.17(nm)

t=

time, (s)

u=

horizontal velocity, (m/s)

v=

vertical velocity, (m/s)

x&y=

cartesian coordinates, (m)

ρ=

density, (kg/m3)

μ=

dynamic viscosity, (kg/ms)

ν=

kinematic viscosity, (m2/s)

α=

thermal diffusivity, (m2/s)

β=

thermal expansion coefficient, (1/K)

τ=

lattice relaxation time

ϕ=

nanoparticle volume fraction, (%)

Π=

heat function

T=

temperature gradient, (K/m)

ϕ=

concentration gradient, (% /m)

θ=

non-dimensional temperature

ΔT=

temperature difference, = (Th − Tc)(K)

Δt=

lattice time step

Subscripts=
T=

temperature

avg=

average

bf=

basefluid

c=

cold

conc=

concentration

h=

hot

i=

discrete lattice direction

lbm=

lattice scale

loc=

local

mom=

momentum

nf=

nanofluid

p=

particle

ref=

reference

temp=

temperature

Superscripts=
eq=

equilibrium

t=

transpose

Acknowledgment

The authors would like to thank P.G. Senapathy Computing Centre, IIT Madras, for providing access to VIRGO SUPER CLUSTER for the simulation. The authors would also like to acknowledge the useful technical discussions and inputs on LBM from Dr. Martin Geier, during his DAAD-IIT faculty exchange stay at IIT Madras.

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