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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 69, 2016 - Issue 10
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Original articles

Numerical simulation and optimization of turbulent nanofluids in a three-dimensional wavy channel

, &
Pages 1169-1185 | Received 07 Jul 2015, Accepted 28 Aug 2015, Published online: 23 Mar 2016
 

ABSTRACT

In this study, numerical calculations by single- and two-phase models of nanofluid turbulent forced convection in a three-dimensional wavy channel with uniform wall temperature are investigated. The numerical results for the Nusselt number ratio (Nu/Nu0) show that the heat transfer performance of a symmetric wavy channel performs better than that of an in-line wavy channel. The multi-parameter constrained optimization procedure integrating the design of experiments (DOEs), response surface methodology (RSM), genetic algorithm (GA), and computational fluid dynamics (CFD) is proposed to design the nanofluid turbulent convection of the three-dimensional wavy channel.

Nomenclature

a=

wave amplitude, mm

A=

acceleration, m/s2

=

closure coefficients

Cp=

specific heat, J/kg · K

Cf=

friction coefficient

Dh=

hydraulic diameter, mm

fdrag=

drag function

g=

gravity acceleration, m/s2

h=

heat transfer coefficient

k=

thermal conductivity, W/m · K

k=

turbulent kinetic energy, m2/s2

Lin=

upstream length, mm

Lw=

wavelength, mm

Lout=

downstream length, mm

Ltotal=

total length, mm

=

average Nusselt number

Nu=

local Nusselt number

P=

pressure, Pa

ΔPo=

pressure drop of the smooth channel, Pa

ΔP=

pressure drop, Pa

PF=

performance factor

q=

heat flux

Re=

Reynolds number,

T=

temperature, K

Tin=

inlet temperature, K

V=

velocity, m/s

u, v, w=

velocity components

x, y, z=

Cartesian x, y, z-coordinates, mm

A=

dimensionless wave amplitude,

λ=

dimensionless wave length,

ρ=

density of the working fluid, kg/m3

μ=

dynamic viscosity, kg/m · s

τ=

shear stress, Pa

φ=

volume fraction

ϵ=

turbulent energy dissipation rate,

σk, σϵ=

empirical constants in turbulence model equations

Subscripts=
dr=

drift

eff=

effective

bf=

base fluid

in=

inlet

m=

mixture

nf=

nanofluid

p=

solid particle

pw=

pure water

w=

wall

Nomenclature

a=

wave amplitude, mm

A=

acceleration, m/s2

=

closure coefficients

Cp=

specific heat, J/kg · K

Cf=

friction coefficient

Dh=

hydraulic diameter, mm

fdrag=

drag function

g=

gravity acceleration, m/s2

h=

heat transfer coefficient

k=

thermal conductivity, W/m · K

k=

turbulent kinetic energy, m2/s2

Lin=

upstream length, mm

Lw=

wavelength, mm

Lout=

downstream length, mm

Ltotal=

total length, mm

=

average Nusselt number

Nu=

local Nusselt number

P=

pressure, Pa

ΔPo=

pressure drop of the smooth channel, Pa

ΔP=

pressure drop, Pa

PF=

performance factor

q=

heat flux

Re=

Reynolds number,

T=

temperature, K

Tin=

inlet temperature, K

V=

velocity, m/s

u, v, w=

velocity components

x, y, z=

Cartesian x, y, z-coordinates, mm

A=

dimensionless wave amplitude,

λ=

dimensionless wave length,

ρ=

density of the working fluid, kg/m3

μ=

dynamic viscosity, kg/m · s

τ=

shear stress, Pa

φ=

volume fraction

ϵ=

turbulent energy dissipation rate,

σk, σϵ=

empirical constants in turbulence model equations

Subscripts=
dr=

drift

eff=

effective

bf=

base fluid

in=

inlet

m=

mixture

nf=

nanofluid

p=

solid particle

pw=

pure water

w=

wall

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