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

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.

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Abbreviations

A 1 :

Porosity ratio

A 2 :

Thermal conductivity ratio

A 3 :

Particle area ratio

A pe :

Wetted area per volume

C :

correction factor

C p :

Specific heat in constant pressure

\(\dot Q\) :

Volume flow rate of heat sink (m3/s)

g 1–9 :

Constants in trial function

Da:

Darcy number

d p :

Nanoparticles diameter

f :

Friction factor

h :

Convection heat transfer coefficient

K :

permeability

k :

Thermal conductivity

k b :

Boltzmann constant

L :

length

\(\tilde u\) :

Trial function

δ:

Distance

u m :

Mean fluid velocity

W(x):

Weighted function

X :

Horizontal axes coordinate

Y :

Vertical axes coordinate

V B :

Brownian velocity

y :

Dimensionless vertical coordinate

d f :

Fluid particle diameter

α s :

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

q w :

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

ch:

channel

f:

fluid

fin:

fin

nf:

nanofluid

p:

particle

hs:

heat sink

s:

solid

w:

wall

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Correspondence to M. Rahimi-Gorji.

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Rahimi-Gorji, M., Pourmehran, O., Hatami, M. et al. Statistical optimization of microchannel heat sink (MCHS) geometry cooled by different nanofluids using RSM analysis. Eur. Phys. J. Plus 130, 22 (2015). https://doi.org/10.1140/epjp/i2015-15022-8

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Keywords

  • Heat Transfer
  • Nusselt Number
  • Response Surface Methodology
  • Galerkin Method
  • Friction Factor