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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 71, 2017 - Issue 7
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Original Articles

The effects of nanoparticle aggregation on the convection heat transfer investigated by a combined NDDM and DPM method

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Pages 754-768 | Received 13 Dec 2016, Accepted 03 Mar 2017, Published online: 27 Apr 2017
 

ABSTRACT

In this study, convective heat transfer of Al2O3-water nanofluids (NFs) of various concentrations under laminar flow in a horizontal circular tube with and without considering particle aggregation was numerically investigated by a combined nanoparticle diameter distribution model (NDDM) with the Discrete Phase Model (DPM). Heat transfer coefficient (h), temperature distribution in axial and radial direction, and pressure drop (ΔP) were studied. It turns out that beside a slight pressure drop, heat transfer near the wall will significantly deteriorate when particle aggregation occurs. With an increase in Re numbers, the effects of particle aggregation on the heat transfer performance of the fluid will decrease.

Nomenclature

Al2O3=

aluminum oxide (alumina)

Tb=

base fluid temperature

c=

heat capacity

Vi=

nanoparticle volume fraction

Cc=

Cunningham correction factor

vb=

base fluid velocity

Df=

fractal dimension

vp=

particle velocity

Fd=

drag force

vb=

viscosity of the fluid

Fg=

gravity force

vc,j=

collision volume of the aggregate

Fb=

Brownian force

FT=

thermophoresis force

Fv=

force due to lift motion

η=

variety of correlations between the particle volume fraction and suspension viscosity

Fl=

force due to virtual mass

η0=

viscosity of the basic fluid of dilute solution

Fp=

force due to pressure gradient

Фtot=

effective of total volume concentration of the aggregate

G=

shear rate

βi,j=

collision rate of particles

g=

acceleration of gravity

σ=

equivalent diameter

h=

heat transfer coefficient (w/m2k)

λ=

molecular mean free path of fluid

I=

unit vector

ζi=

unit-variance-independent Gaussian random number with zero-mean

k=

thermal conductivity

λ0=

nanofluid thermal conductivity

Kn=

Knudsen number

φ=

nanofluids concentration

kB=

Boltzmann constant

αb=

stress tensor

Nu=

Nusselt number

μb=

shear viscosity of the fluid phase

Ni=

number concentration of flocs

xi=

number of primary particle in section i

p=

pressure

Γi,j=

fragment distribution function

ΔP=

pressure drop

ρb=

base fluid density

Pr=

Prandtl number

ρp=

particle density

Re=

Reynold number

Subscripts=
Si=

rate of particle breakage

b=

base fluid

Sp=

source term

p=

particle

Si=

rate of particle breakage

tot=

total

t=

time

Tp=

particle temperature

Nomenclature

Al2O3=

aluminum oxide (alumina)

Tb=

base fluid temperature

c=

heat capacity

Vi=

nanoparticle volume fraction

Cc=

Cunningham correction factor

vb=

base fluid velocity

Df=

fractal dimension

vp=

particle velocity

Fd=

drag force

vb=

viscosity of the fluid

Fg=

gravity force

vc,j=

collision volume of the aggregate

Fb=

Brownian force

FT=

thermophoresis force

Fv=

force due to lift motion

η=

variety of correlations between the particle volume fraction and suspension viscosity

Fl=

force due to virtual mass

η0=

viscosity of the basic fluid of dilute solution

Fp=

force due to pressure gradient

Фtot=

effective of total volume concentration of the aggregate

G=

shear rate

βi,j=

collision rate of particles

g=

acceleration of gravity

σ=

equivalent diameter

h=

heat transfer coefficient (w/m2k)

λ=

molecular mean free path of fluid

I=

unit vector

ζi=

unit-variance-independent Gaussian random number with zero-mean

k=

thermal conductivity

λ0=

nanofluid thermal conductivity

Kn=

Knudsen number

φ=

nanofluids concentration

kB=

Boltzmann constant

αb=

stress tensor

Nu=

Nusselt number

μb=

shear viscosity of the fluid phase

Ni=

number concentration of flocs

xi=

number of primary particle in section i

p=

pressure

Γi,j=

fragment distribution function

ΔP=

pressure drop

ρb=

base fluid density

Pr=

Prandtl number

ρp=

particle density

Re=

Reynold number

Subscripts=
Si=

rate of particle breakage

b=

base fluid

Sp=

source term

p=

particle

Si=

rate of particle breakage

tot=

total

t=

time

Tp=

particle temperature

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