1. A Thesis
Submitted to the Faculty of Inha University
In Partial Fulfillment of the Requirements
for the Degree of
Doctor of Philosophy in Mechanical Engineering
Numerical Analysis and Design Optimization of
Pressure- and Electroosmotically-Driven Liquid
Flow Microchannel Heat Sinks
by
Afzal Husain
under the supervision of
Prof. Kwang-Yong Kim
Mechanical Engineering Department,
Inha University, Korea
Nov. 16 & 30, 2009
2. Microchannel Heat Sink (MCHS)
• Silicon-based microchannels to be fabricated at the inactive side
of a chip.
• Typical dimensions 10mm×10mm
• Typical number of channels ≈ 100, and Heat flux: q = 100W/cm2
• Coolant : Deionized Ultra-Filtered (DIUF) Water
Air ly
To Air heat Ti
Exchanger lx
Silicon Channels with
glass cover plate
Pump
q
Liquid hc
Microchannel lz
heat sink Ti wc ww z
To x
q
y
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3. Background: MCHS (1)
• Microchannel heat sink (MCHS) has been proposed as an
efficient device for electronic cooling, micro-heat exchangers
and micro-refrigerators etc.
• Experimental studies have been carried out and low-order
analytical and numerical models have been developed with
certain assumptions to understand the heat transfer and fluid
flow in the MCHS.
• A full model numerical analysis has been proposed as one of
the most accurate theoretical techniques available for evaluating
the performance of the MCHS.
• The growing demand for higher heat dissipation and
miniaturization have focused studies to efficiently utilize the
silicon material, space and to optimize the design of MCHS.
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4. Background: MCHS (2)
• Alternative designs other than the smooth MCHS had been
proposed to enhance the performance of MCHS.
• The growing demand for higher heat flux has raised issues
of limiting pumping power at micro-scale.
Characteristics of
various micropumps
(Joshi and Wei 2005)
Limiting values
Back pressure < 2 bar
Flow rate < 35 ml/min
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5. Motivation (1)
• For a steady, incompressible and fully developed laminar flow:
hd h 1
Nusselt Number = = const.
Nu and h∝
k dh
d h .∆p
Friction factor =f = const.
2 ρ u 2l x
2
wc
( f Re) µlx .Q. 1 +
Re µlx .Q 1
Pressure drop ∆p 2 f= hc
= . 2
wc hc dh 2 wc 3hc
wc ∆p 1
For and Q = const. we have ∝ 4
hc lx hc
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6. Motivation (2)
• The lack of studies on systematic optimization of full model
MCHS which could provide a wide perspective for designers
and thermal engineers.
• Although the single objective optimization (SOO) has its
own advantages, a multi-objective optimization (MOO)
could be more suitable while dealing with multiple
constraints and multiple objectives.
• Three-dimensional full model numerical analyses require
high computational time and resources therefore surrogate
models could be applied to microfluidics as well.
• The limitations with the current state-of-the-art micropumps
motivated the application of unconventional methods of
driving fluid through microchannels.
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7. Objectives
• To optimize the performance of various designs of MCHSs in
view of fabrication and flow constraints using gradient based
as well as evolutionary algorithms.
• To enhance the performance of the MCHS through passive
micro-structures applied on the walls of the microchannels.
• To develop surrogate-based optimization models for the
application to microfluidics.
• To apply multi-objective evolutionary algorithm (MOAE)
coupled with surrogate models to economize optimization
procedure.
• To enhance the performance of the MCHSs through
unconventional pumping methods, e.g., electroosmosis.
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9. Rectangular and Trapezoidal MCHS
A MCHS of 10mm×10mm is set to be characterized and
optimized for minimum pumping power and thermal resistance at
constant heat flux.
Microchannel heat sink
Design variables
ly
θ = wc / hc
φ = ww / hc
lx Computational
domain Cover plate η = wb / wc
ww wc
wb = wc Rect.
hc lz
wb z 0 < wb < wc Trap.
Half pitch x
y
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10. Boundary Conditions
Outflow
Symmetric boundary
Adiabatic boundaries
Symmetric boundaries
Silicon substrate q
Heat flux
Inflow
Computational domain
Half pitch of the microchannel
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11. Roughened (Ribbed) MCHS
A roughened (ribbed) MCHS is designed and optimized to
minimize thermal resistance and pumping power.
wc = 70 µ m Outflow
ww = 30 µ m
Design variables
hc = 400 µ m
α = hr / wc
β = wr / hr
γ = wc / pr
Inflow Computational domain
One of the parallel channels
q Heat flux
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13. Numerical Scheme PDF (1)
• Silicon-based MCHS with deionized ultra-filtered (DIUF) water
as coolant.
• A steady, incompressible, and laminar flow simulation.
• Finite-volume analysis of three-dimensional Navier-Stokes and
energy equations.
• An overall mesh-system of 401×61×16 was used for a 100µm
pitch for smooth rectangular MCHS after carrying out grid-
independency test.
• A 501×61×41 grid was used for roughened (ribbed) MCHS
after carrying out grid-independency test.
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14. Numerical Scheme PDF (2)
Mathematical Formulation
Pumping power P = Q.∆p = n.uavg . Ac .∆p
Global thermal ∆Tmax
resistance Rth =
qAs
Maximum temperature ∆Tmax =Ts ,o − T f ,i
rise
Fanning friction Re f = γ
factor
2.α 1
Average velocity uavg = . .P
γµ f (α + 1) n.Lx
2
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15. Numerical Scheme EOF
• Electroosmotic force due to electric field in the presence of
electric double layer (EDL) can be treated as a body force in
the Navier-Stokes equations:
(u ⋅∇) ρ u = −∇p + ∇.( µ∇u) + ρe E
• Poisson-Boltzmann equation: 2n∞ zb e zb e
∇ψ
= 2
sinh − ψ
ε kbT
• Poisson-Boltzmann equation is solved numerically using
finite volume solver.
• Linearized Poisson-Boltzmann ∇ 2ψ = κ 2ψ
Equation:
• Linearized Poisson-Boltzmann equation is solved through
analytical technique:
• Energy equation: u.∇( ρ c pT ) =.(k ∇T ) + E 2 ke
∇
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17. Single Objective Optimization Technique
(Problem setup)
Optimization procedure Design variables & Objective function
(Design of experiments)
Selection of design points
Objective function
(Numerical Analysis)
Determination of the value of objective
function at each design points
F = Rth (Construction of surrogate )
RSA, KRG and RBNN Methods
(Search for optimal point)
Optimal point search from constructed
Constraint surrogate using optimization algorithm
Is optimal point No
within design space?
Pumping power
Yes
Optimal Design
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20. 1-Smooth Microchannels
Design Space: Rectangular and Trapezoidal MCHSs
• Design points are selected using four-level full factorial design.
Design variables Lower limit Upper limit
hc = 400 µ m wc/hc (=θ ) 0.1 0.25
ww/hc (=φ ) 0.04 0.1
• Design points are selected using three-level fractional factorial
design.
Design variables Lower limit Upper limit
wc/hc (=θ ) 0.10 0.35
hc = 370 µ m
ww/hc (=φ ) 0.02 0.14
wb/wc (=η ) 0.50 1.00
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21. 2-Roughened (Ribbed) Microchannel
Roughened (ribbed) MCHS with three design variables
• Design points are selected using three-level fractional
factorial design.
Design variables Lower limit Upper limit
wc = 70 µ m
hr /wc (=α ) 0.3 0.5
ww = 30 µ m
wr /hr (=β) 0.5 2.0
hc = 400 µ m
wc /pr (=γ) 0.056 0.112
• Surrogates are constructed using objective function values
which are calculated through numerical simulation at each
design point defined by Design of Experiments (DOE).
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23. Numerical Validation PDF (1)
• Comparison of numerical simulation results with experimental
results of Tuckerman and Pease (1981).
Case1 Case2 Case3
wc (µm) 56 55 50
ww (µm) 44 45 50
hc (µm) 320 287 302
h (µm) 533 430 458
q (W/cm2) 181 277 790
Rth (oC/W)
0.110 0.113 0.090
Exp.
Rth (oC/W)
0.116 0.105 0.085
CFD cal.
% Error 5.45 7.08 5.55
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24. Numerical Validation PDF (2)
• Comparison of numerically simulated thermal resistances with
experimental results for smooth MCHS (Kawano et al. 1998).
Kawano et al. (1998)
0.5 Present model
Rth,o (K/W)
0.3
0.1
100 200 300 400
Re
Outlet thermal resistance
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25. Numerical Validation EOF
• Validation of present model for pressure driven flow
(PDF) and electroosmotic flow (EOF)
14
Arulanandam and Li (2000)
Volume flow rate (l min )
-1
Morini et al. (2006) Morini (1999) slug flow
5E-05 Present model EOF
12 Present model EOF
Nufd
3E-05 10
8
1E-05
6
5E-05 0.0001 0.00015 0.0002 0.00025 0.15 0.2 0.25
dh (m) θ
θ = wc / hc
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32. Single Objective Optimization PDF (1)
Smooth Rectangular MCHS:
• Comparison of optimum thermal resistance at constant heat
flux and pumping power using Kriging model (KRG) with
reference design.
• Two design variables consideration.
θ φ Rth
Models
wc/hc ww/hc (CFD calculation)
Tuckerman and
0.175 0.138 0.214
Pease (1981)
Optimized 0.174 0.053 0.171
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33. Single Objective Optimization PDF (2)
Smooth Trapezoidal MCHS:
• Optimum thermal resistance using Radial Basis Neural
Network (RBNN) model at constant heat flux and pumping
power.
• Three design variables consideration.
θ φ η Rth (Surrogate Rth (CFD
Model
wc/hc ww/hc wb/wc pred.) cal.)
Kawano et al.
0.154 0.116 1.000 0.1988 0.1922
(1998)
Present 0.249 0.036 0.750 0.1708 0.1707
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34. Single Objective Optimization PDF (3)
Smooth Trapezoidal MCHS:
• Sensitivity of objective function with design variables.
0.02
θ θ
φ 0.0012 φ
η
(Rth-Rth,opt)/Rth,opt
η
(Rth-Rth,opt)/Rth,opt
0.01
0.0008
0
0.0004
-0.01
0
-10 -5 0 5 10 -10 -5 0 5 10
Deviation from Optimal Point (%) Deviation from Optimal Point (%)
Kawano et al. (1998) Optimized
= wc / hc , φ ww / hc= wb / wc
θ = and η
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35. Multi-objective Optimization PDF (1)
Smooth Rectangular MCHS:
• Multiobjective optimization using MOEA and RSA
(Response Surface Approximation).
0.16
NSGA-II
Thermal Resistance (K/W)
A Hybrid method
0.14 Clusters
POC
Pareto-optimal
0.12
B Front
0.1
C
0.08
0 0.2 0.4 0.6 0.8
Pumping Power (W)
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36. Multi-objective Optimization PDF (2)
Smooth Trapezoidal MCHS:
• Multiobjective optimization using MOEA and RSA.
• Pareto-optimal front.
0.15 Hybrid method
x
x
7 x
7 Clusters
x
x
x
x
x
x
x
x
x
x
NSGA-II
xx
x
6
x
0.13 x
x
x
Rth (K/W)
x
x
x
x
x
x
x
POC
x
x
x
x
x
5
x
x
0.11
x
x
x
x
x
x
x
4
x
x
x
x
x
x
x
x
3
x
x
xx
x
x x
x x
x
x x
0.09 2
x x
xx
x x
xx
x x
1
x x
x x
x x
xx
x x
x
x x
x x
x x
xx
x xx x
x x x
x x x x x x x x
0.07
0 0.5 1 1.5
P (W)
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37. Multi-objective Optimization PDF (3)
Trapezoidal MCHS:
• Sensitivity of objective functions to design variables along
Pareto-optimal front.
1 1 θ
φ
η
Design Variables
Design Variables
0.8 0.8
0.6 7 0.6 7
0.4 6 0.4 6
0.2 θ 0.2
5 φ
5 2
12 3 4 4 3 1
0 η 0
0.08 0.1 0.12 0.14 0 0.5 1 1.5
Rth (K/W) P (W)
= wc / hc , φ ww / hc= wb / wc
θ = and η
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38. Multi-objective Optimization PDF (4)
Roughened (ribbed) MCHS:
• Multiobjective optimization using MOEA and RSA.
• Pareto-optimal front.
0.188
C
Thermal Resistance (K/W)
NSGA-II
0.184
Hybrid Method
Clusters
POC
0.18
B
0.176
A
0.172
0.04 0.06 0.08 0.1 0.12
Pumping Power (W)
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40. Single Objective Optimization EOF
• Design variables at different optimal points obtained at various
values of pumping source for combined flow (PDF+EOF).
Ex θ φ
Δp (kPa) Rth (K/W)
(kV/cm) wc/hc ww/hc
7.5 10 0.250 0.060 0.1865
7.5 15 0.250 0.062 0.1799
7.5 20 0.250 0.062 0.1776
10 10 0.249 0.078 0.1703
15 15 0.185 0.066 0.1435
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41. Multi-objective Optimization EOF
• Pareto-optimal front with representative cluster solutions
at dp=15kPa and EF=10kV/cm.
0.045 NSGA-II (PDF+EOF)
A Clusters (PDF+EOF)
0.035
P (W)
B
0.025
C
0.015 D
E
0.005
0.15 0.2 0.25
Rth (K/W)
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43. Conclusions (1)
• The ratio of microchannel width-to-depth is the most and ratio
of fin width-to-depth of microchannel is the least sensitive to
thermal resistance and pumping power.
• Ribbed MCHS: the application of the rib-structures in the
MCHSs strongly depends upon the design conditions and
available pumping source.
• The prediction of objective function values by the surrogate
models are close to the numerically calculated values which
suggests the scope for the surrogate-based optimization
techniques in microfluidic as well.
• Surrogate-based optimization techniques can be utilized to
microfluidic systems to effectively reduce the optimization
time and expenses.
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44. Conclusions (2)
• The Pareto-optimal front obtained through multi-objective
evolutionary algorithm offers useful trade-offs between
thermal resistance and pumping power.
• Multi-objective evolutionary algorithms (MOEA) coupled
with surrogate models can be applied to economize
comprehensive optimization problems of microfluidics.
• The bulk fluid driving force generated by electroosmosis
can be effectively utilized to assist the existed driving
source.
• The thermal resistance of the MCHS can be significantly
reduced by the application of electric potential in the
presence of electric double layer (EDL).
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47. Comments and Suggestions
1. Explanation of various terms in the expression of overall
thermal resistance.
2. Correction of Co-ordinate systems for Figures.
3. Explicit mention of velocity approximate/empirical
relations.
4. Repetitive sentences in the model descriptions and results
and discussion.
5. Roughened microchannel and ribbed microchannel
6. Corrections in the Korean Abstract.
7. There were some formatting mistakes.
8. Thesis-Title modification.
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48. Comments and Suggestions
1. Explanation of various terms of overall thermal resistance:
Rth = Rth ,cond + Rth ,conv + Rth ,cal
t 1 1
= =
Rth ,cond , Rth ,conv = and Rth ,cal
k s l xl y hA fs
mc p f
2. Co-ordinate system for Figs.
x
ly ly
y
lx z lx
Cover plate Cover plate
hc hc
lz lz
wc ww z wc ww
x
y
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49. Comments and Suggestions
3(a). The explicit mention about the approximate expression
used for calculating velocity at constant pumping power for
rectangular MCHS: Knight et al. (1992) approximated that
(θ 2 + 1)
G= f = 4.70 + 19.64G
Re
(θ + 1) 2
3(b). Again London and Shah (1978) proposed empirical
relation
f Re = − 1.3553θ + 1.9467θ 2 − 1.7012θ 3
24(1
+ 0.9564θ 4 − 0.2537θ 5 )
2θ 1
uavg = P
f Re µ f (θ + 1) nm .lx
2
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50. Comments and Suggestions
4. Repetitive Discussion:
The repetitive discussion has been corrected at various
locations
5. Roughened microchannel has been replaced with ribbed
microchannel.
6. Formatting Comments:
The various formatting mistakes have been corrected.
7. Abstract in Korean language has been Corrected.
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51. Comments and Suggestions
8. Thesis-Title Modification
Original Title
Microchannel Heat Sinks: Numerical Analysis and Design
Optimization
Modified Titles
1- Numerical Analysis and Design Optimization of Pressure- and
Electroosmotically-Driven Liquid Flow Microchannel Heat sinks
2- Numerical Analysis and Design Optimization of Pressure-Driven
and Electroosmotic Liquid Flow Microchannel Heat Sinks
3- Numerical Analysis and Design Optimization of Pressure-Driven
and Electroosmotic Flow Microchannel Heat Sinks
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52. Comments and Suggestions
Selected Title
Numerical Analysis and Design Optimization of Pressure- and
Electroosmotically-Driven Liquid Flow Microchannel Heat sinks
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