Accepted Manuscript Numerical investigation into the thermo-fluid performance of wavy microchannels with superhydrophobic walls Hamidreza Ermagan, Roohollah Rafee PII: DOI: Reference:
S1290-0729(18)30526-X https://doi.org/10.1016/j.ijthermalsci.2018.06.035 THESCI 5517
To appear in:
International Journal of Thermal Sciences
Received Date: Revised Date: Accepted Date:
23 March 2018 8 June 2018 29 June 2018
Please cite this article as: H. Ermagan, R. Rafee, Numerical investigation into the thermo-fluid performance of wavy microchannels with superhydrophobic walls, International Journal of Thermal Sciences 132 (2018) 578-588, doi: https://doi.org/10.1016/j.ijthermalsci.2018.06.035
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© 2018. This manuscript version is made available under the CC-BY-NCND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
H. Ermagan, R. Rafee, Numerical investigation into the thermo-fluid performance of wavy microchannels with superhydrophobic walls, International Journal of Thermal Sciences 132 (2018) 578-588
https://doi.org/10.1016/j.ijthermalsci.2018.06.035
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Numerical Investigation into the Thermo-Fluid Performance of
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Wavy Microchannels with Superhydrophobic walls
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Hamidreza Ermagan, Roohollah Rafee*
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Faculty of Mechanical Engineering, Semnan University, Semnan, Iran
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Abstract
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As an efficient cooling method, wavy microchannel heat sink (W-MCHS) with
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superhydrophobic walls is suggested as an alternative to a straight microchannel heat sink
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(S-MCHS) with conventional walls. Navier-Stokes and Energy equations with slip
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boundary conditions (velocity slip and temperature jump) are solved to study the hydraulic
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and thermal performances of the microchannels. It is observed that based on the “goodness
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factor” criterion, the overall performance of the new heat sink design is improved by 47.3%.
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In fact, the pressure drop reduction accompanying the use of superhydrophobic walls
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outweighs the thermal performance degradation due to the presence of trapped layers of air.
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It is also observed that with an increase in the waviness of the channel (either by an increase
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in the wave amplitude or a decrease in the wavelength), the pressure drop reduction by the
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use of superhydrophobic walls intensifies as the maximum velocity shifts from the centre
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of the channel towards the crest regions. This, in turn, increases the velocity gradient at the
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wall which excites the velocity slip and results in a better hydraulic performance. On the
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other hand, the thermal performance is deteriorated to a greater extent (compared to the
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hydraulic improvement) when the channel waviness increases, due to the elongated flow
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path and the related increase in the trapped layers of air. As a result, as long as the cooling
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performance of the heat sink with superhydrophobic walls is concerned, microchannels with
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lower waviness are desirable.
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Keywords: Heat sink, Wavy microchannels, Superhydrophobic walls, Goodness factor, Slip
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boundary conditions, Overall performance enhancement.
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*
Corresponding author, E-mail address:
[email protected], P.O.B.:35131-19111.
© 2018. This manuscript version is made available under the CC BY NC ND 4.0 license
http://creativecommons.org/licenses/by-nc-nd/4.0/
H. Ermagan, R. Rafee, Numerical investigation into the thermo-fluid performance of wavy microchannels with superhydrophobic walls, International Journal of Thermal Sciences 132 (2018) 578-588
https://doi.org/10.1016/j.ijthermalsci.2018.06.035
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Nomenclature
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A
Wave amplitude (m)
W
channel width (m)
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Cp
specific heat (J kg-1 K-1)
Wfin
fin width (m)
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Dh
hydraulic diameter (m)
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f
average friction factor (-)
Greek symbols
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h
convective heat transfer coefficient (W m-2 K-1)
δ
substrate thickness (m)
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H
channel height (m)
λ
wavelength (m)
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lS
slip length (m)
µ
dynamic viscosity (kg m-1 s-1)
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Lx
length of the heat sink (m)
ξS
temperature jump coefficient (m)
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Ly
width of the heat sink (m)
ρ
density (kg m-3)
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Lz
height of the heat sink (m)
φ
goodness factor (-)
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n
wall normal vector
ρ
density (kg m-3)
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Nu
average Nusselt number
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p
pressure (Pa)
Subscript
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q
heat flux (W m-2)
f
fluid
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Q
volumetric flow rate (m3 s-1)
m
mean
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Re
Reynolds number
s
solid
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S
heat transfer surface
w
wall
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T
temperature
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uin
inlet velocity (m s-1)
Superscript
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V
velocity vector (m s-1)
*
dimensionless values
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1. Introduction
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Fluid flow and heat transfer in micro scale geometries have been the subject of extensive
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studies during the past three decades [1,2], making significant contribution to the
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development of Micro-Electro-Mechanical Systems (MEMS) [3], microfluidic devices [4]
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and bio-microsystems [5]. Wavy microchannels, being no exception, have aroused
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researchers’ interests ever since their capabilities of high heat flux removal [6,7], superior © 2018. This manuscript version is made available under the CC BY NC ND 4.0 license
http://creativecommons.org/licenses/by-nc-nd/4.0/
H. Ermagan, R. Rafee, Numerical investigation into the thermo-fluid performance of wavy microchannels with superhydrophobic walls, International Journal of Thermal Sciences 132 (2018) 578-588
https://doi.org/10.1016/j.ijthermalsci.2018.06.035
56
mixing index [8,9], and filter performance improvement [10] were highlighted. Thanks to
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the emergence of secondary flows due to the centrifugal forces, wavy microchannels show
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higher convective fluid mixing, and hence, higher heat transfer coefficient compared to
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straight microchannels [6]. Based on this premise, wavy microchannel heat sink (W-MCHS)
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is suggested as an alternative to the conventional straight MCHS (S-MCHS) initially
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proposed by Tuckerman and Pease [11].
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Rush et al. [12] examined the fluid flow and heat transfer in wavy microchannels for
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Reynolds (Re) number below 1000. They observed that for a relatively low Re (~200),
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instabilities occur initially at the channel exit. These instabilities were found to emerge in
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the upstream regions when Re was increased. Sui et al. [6] numerically investigated liquid
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flow and thermal transport in a W-MCHS. In their study, Re number was kept below 800 in
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order to maintain flow in a steady-state regime. They observed that the change in the patterns
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of Dean Vortices along the microchannels are accountable for the chaotic advection and the
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concomitant increase in heat transfer coefficient. In another work [13], they experimentally
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investigated thermal-hydraulic performance of a W-MCHS for Re numbers from 300 to
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800. Wave amplitude of the wall was varied between 0, corresponding to an S-MCHS, up
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to 260 μm. They showed that numerical prediction based on classical steady state Navier-
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Stokes and energy equations with no-slip boundary conditions could accurately predict the
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obtained experimental data.
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Although aforementioned studies seem to limit thermal improvement in wavy passages
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to high Re flows, some studies suggested considerable thermal enhancement at medium Re
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flows (50
