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Statistical optimization of microchannel heat sink (MCHS) geometry cooled by different nanofluids using RSM analysis

  • M. Rahimi-Gorji
  • O. Pourmehran
  • M. Hatami
  • D. D. Ganji
Regular Article

Abstract

In this work, an analytical investigation of the heat transfer for the microchannel heat sink (MCHS) cooled by different nanofluids (Cu, Al2O3, Ag, TiO2 in water and ethylene glycol as base fluids) is studied by the porous media approach and the Galerkin method and results are compared with numerical procedure. Response surface methodology (RSM) is applied to obtain the desirability of the optimum design of the channel geometry. The effective thermal conductivity and viscosity of the nanofluid are calculated by the Patel et al. and Khanafer et al. model, respectively, and MCHS is considered as a porous medium, as proposed by Kim and Kim. In addition, to deal with nanofluid heat transfer, a model based on the Brownian motion of nanoparticles is used. The effects of the nanoparticles volume fraction, nanoparticle type and size, base fluid type, etc., on the temperature distribution, velocity and Nusselt number are considered. Results show that, by increasing the nanoparticles volume fraction, the Brownian movement of the particles, which carries the heat and distributes it to the surroundings, increases and, consequently, the difference between coolant and wall temperature becomes less.

Keywords

Heat Transfer Nusselt Number Response Surface Methodology Galerkin Method Friction Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

A1

Porosity ratio

A2

Thermal conductivity ratio

A3

Particle area ratio

Ape

Wetted area per volume

C

correction factor

Cp

Specific heat in constant pressure

\(\dot Q\)

Volume flow rate of heat sink (m3/s)

g1–9

Constants in trial function

Da

Darcy number

dp

Nanoparticles diameter

f

Friction factor

h

Convection heat transfer coefficient

K

permeability

k

Thermal conductivity

kb

Boltzmann constant

L

length

\(\tilde u\)

Trial function

δ

Distance

um

Mean fluid velocity

W(x)

Weighted function

X

Horizontal axes coordinate

Y

Vertical axes coordinate

VB

Brownian velocity

y

Dimensionless vertical coordinate

df

Fluid particle diameter

Greek symbols

αs

channel aspect ratio

μ

viscosity

ε

porosity

ρ

density

ReB

Brownian Reynolds number

N

Number of channel

Nu

Nusselt number

P

pressure

p

Power law index

Pr

Prandtl number

qw

Heat flux

Re

Reynolds number

R(x)

Residual function

T

Temperature

U

Dimensionless velocity

u

velocity

ϕ

Nanoparticles volume fraction

θ

Dimensionless temperature

ν

Kinematic viscosity

Subscripts

ch

channel

f

fluid

fin

fin

nf

nanofluid

p

particle

hs

heat sink

s

solid

w

wall

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Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • M. Rahimi-Gorji
    • 1
  • O. Pourmehran
    • 1
  • M. Hatami
    • 2
  • D. D. Ganji
    • 1
  1. 1.Mechanical Engineering DepartmentBabol University of TechnologyBabol, MazandaranIran
  2. 2.Mechanical Engineering DepartmentEsfarayen University of TechnologyEsfarayen, North KhorasanIran

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