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
Microchannel Heat Sinks: Numerical Analysis
and Design Optimization
by
Afzal Husain
under the supervision of
Prof. Kwang-Yong Kim
Mechanical Engineering Department,
Inha University, Korea
Nov. 16, 2009

2. Introduction
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3. Microchannel Heat Sink (MCHS)
• Silicon-based microchannels with glass cover plate
• Typical dimensions 10mm×10mm×0.5mm
• Heat flux: q = 100 W/cm2
• Typical number of channels = 100
• Coolant : Deionized Ultra-Filtered (DIUF) Water
ly
lx
Silicon Channels with
glass cover plate
q
hc lz
wc ww z
x
y
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4. Background: MCHS (1)
• Microchannel heat sink (MCHS) has been proposed as an
efficient cooling 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 phenomena in the MCHS.
• A full model numerical analysis has been proposed as the
most accurate theoretical technique which are available to
evaluate 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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5. Background: MCHS (2)
• Alternative designs other than the smooth MCHS had been
proposed to enhance the performance of microchannel heat
sink.
• The growing demand for higher heat flux has been 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: 50 ml/min
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6. 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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7. 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 could be
more suitable while dealing with multiple constraints and
multiple objective functions.
• The 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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8. Objectives (1)
• Performance analysis of various designs of MCHSs, e.g.,
rectangular MCHS, trapezoidal MCHS, roughened MCHS
etc.
• To enhance the performance of the MCHS through passive
micro-structures applied on the walls of the microchannels.
• To optimize the performance of these MCHSs in view of
fabrication complexities of the design and available pumping
power etc. using gradient based as well as evolutionary
algorithms.
• To enhance the performance of the MCHSs through
unconventional pumping methods, e.g., using electroosmotic
flow (EOF) along with pressure-driven flow (PDF).
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9. Objectives (2)
• To develop surrogate-based optimization models for the
application to microfluidics and to characterize and evaluate
performance of MCHS.
• Single- and multi-objective optimization of microchannel
heat sink considering pumping power and thermal resistance
as performance objective functions.
• To apply multi-objective evolutionary algorithm (MOAE)
coupled with various surrogate models to economize
optimization procedure.
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10. Model Definition
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11. Rectangular MCHS
A rectangular MCHS of 10mm×10mm×0.5mm is set to
characterize and optimize for minimum pumping power and
thermal resistance at constant heat flux.
Micro-channel heat sink
ly
Design variables
lx
Cover plate Computational
domain
θ = wc / hc
φ = ww / hc
hc lz
wc ww z
x
Half pitch y
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12. Trapezoidal MCHS
A trapezoidal MCHS of 10mm×10mm×0.42mm is set to
characterize and optimize for minimum pumping power and thermal
resistance at constant heat flux.
Microchannel heat sink
ly
Design variables
lx Computational
domain Cover plate θ = wc / hc
ww wc
φ = ww / hc
hc
η = wb / wc
lz
wb z
Half pitch x
y
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13. 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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14. Roughened (Ribbed) MCHS
A roughened (ribbed) MCHS is designed and optimized to
minimize thermal resistance and pumping power.
Outflow Design variables
α = hr / wc
β = wr / hr
γ = wc / pr
Computational domain
One of the parallel channels
Inflow
q Heat flux
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15. Numerical Scheme
Pressure-driven Flow (PDF)
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16. 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.
• Conjugate heat transfer analysis taking fluid channel and
silicon substrate.
• Unstructured hexahedral mesh.
• Finer mesh for fluid and courser in the solid region.
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17. Numerical Scheme PDF (2)
• An overall mesh-system of 401×61×16 was used for a 100µm
pitch for smooth rectangular MCHS after carrying out grid-
independency test.
• An overall mesh-system of 121×54×16 was used for smooth
trapezoidal MCHS.
• A 501×61×41 grid was used for roughened (ribbed) MCHS
after carrying out grid-independency test.
• A constant heat flux (100 W/cm2) at the bottom of the
microchannel heat sink.
• Thermal resistance and pumping power were calculated at the
sites designed through a DOE in the design space.
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18. Numerical Scheme PDF (3)
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
Friction constant Re f = γ
2.α 1
Average velocity uavg = . .P
γµ f (α + 1) n.Lx
2
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19. Numerical Scheme
Electroosmotic flow (EOF)
and
Combined Flow (PDF+EOF)
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20. Numerical Scheme EOF (1)
• The PDF model of the MCHS has been further investigated
for electroosmotic flow (EOF).
• Poisson-Boltzmann equation is solved for electric field and
electric charge density is evaluated thereafter.
Stern layer Movable layer
EP
+ −
dp
q
Schematic of Electrical Double layer
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21. Numerical Scheme EOF (2)
• Electroosmotic force due electric field in the presence of
electric double layer (EDL) can be treated as body force in
the Navier-Stokes equations:
(u ⋅∇) ρ u = −∇p + ∇.( µ∇u) + ρe E
• Electric Field and Electric Potential: EΦ −∇
=
• Poisson Equation for Electric Potential: ∇ 2Φ = e / ε
−ρ
• Decouple EDL Potential: = φext + ψ
Φ
• Laplace and Poisson Eqns: ∇ 2φext = therefore ∇ 2ψ = e / ε
0 −ρ
• Effective Electric Field: E = ∇φext
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22. Numerical Scheme EOF (3)
• Distribution of electric charge density: ∇ 2ψ = e / ε
−ρ
ze 
• Equilibrium Boltzmann distribution: ni = n∞ exp  b ψ 
 kbT 
 zb e 
• Electric charge density: ρe =  −
−2n∞ zb e sinh ψ
 kbT 
• Poisson-Boltzmann equation: 2n∞ zb e  zb e 
∇ψ
= 2
sinh  − ψ
ε  kbT 
• Poisson-Boltzmann equation is solved numerically using
finite volume solver.
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23. Numerical Scheme EOF (4)
• Linearized Poisson-Boltzmann ∇ 2ψ =
κ 2ψ
Equation:
1/ 2
 2n∞ zb e 
2 2
κ =
εε 0 kbT 
• Debye-Huckel parameter:
 
• Resulting electric charge density: ρe = −εκ 2ψ
• Linearized Poisson-Boltzmann equation is solved through
analytical technique:
• Energy equation: u.∇( ρ c pT ) =.(k ∇T ) + E 2 ke
∇
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24. Models for Optimization
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25. 1-Smooth Microchannel
Rectangular microchannel with two design variables
• Design points are selected using four-level full factorial
design. Number of design points are 16 for construction of
model with two design variables.
Design variables Lower limit Upper limit
wc/hc (=θ ) 0.1 0.25
ww/hc (=φ ) 0.04 0.1
• Surrogate is constructed using objective function values at
these design points.
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26. 2-Smooth Microchannel
Trapezoidal microchannel with three design variables
• Design points are selected using three-level fractional
factorial design.
Design variables Lower limit Upper limit
wc/hc (=θ ) 0.10 0.35
ww/hc (=φ ) 0.02 0.14
wb/wc (=η ) 0.50 1.00
• Surrogate is constructed using objective function values at
these design points.
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27. 3-Rough (Ribbed) Microchannel
Roughened (ribbed) microchannel with three design variables
• Design points are selected using three-level fractional
factorial design.
Design variables Lower limit Upper limit
hr /wc (=α ) 0.3 0.5
wr /hr (=β) 0.5 2.0
wc /pr (=γ) 0.056 0.112
• Surrogate is constructed using objective function values at
these design points.
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28. Optimization Procedure
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29. 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?
Constant pumping power
Yes
Optimal Design
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30. Multi-objective Optimization Technique
Objective Functions Rth and P
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31. Surrogate Models
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32. Surrogate Models (1)
Surrogate Model : RSA
• RSA (Response Surface Approximation): Curve fitting by
regression analysis using computational data.
• Response function: second-order polynomial
n n n
F = ∑ β j x j + ∑ β jj x + ∑
β0 + 2
j ∑β x xj
ij i
= 1= 1
j j i≠ j
where n : number of design variables
x : design variables
β : estimated parameters
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33. Surrogate Models (2)
Surrogate Model : KRG
• KRG (Kriging): Deterministic technique for optimization.
• Linear polynomial function with Gauss correlation function
was used for model construction.
• Kriging postulation: Combination of global model and
departure
F (x) = f(x) + Z(x)
where F(x) : unknown function
f(x) : global model - linear function
Z(x) : localized deviation - realization of a
stochastic process
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34. Surrogate Models (3)
Surrogate Model : RBNN
• RBNN (Radial Basis Neural Network): Two layer
network which consist of a hidden layer of radial basis
function and a linear output layer.
• Design Parameters: spread constant (SC) and user defined
error goal (EG).
• MATLAB function: newrb
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35. Numerical Validation PDF
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36. Numerical Validation PDF (1)
• Comparison of numerically simulated velocity profiles with
analytical data in two different directions for smooth
rectangular microchannel heat sink.
1 1
0.8 0.8
u/umax
u/umax
0.6 0.6
0.4 0.4
Shah and London (1978) Shah and London (1978)
0.2 Present model 0.2 Present model
0 0
0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1
y/ymax z/zmax
Velocity profile in Y-direction Velocity profile in Z-direction
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37. Numerical Validation PDF (2)
• Comparison of numerically simulated thermal resistances
with experimental results for smooth rectangular
microchannel heat sink.
Kawano et al. (1998) Kawano et al. (1998)
Present model 0.5 Present model
0.3
Rth,o (K/W)
Rth,i (K/W)
0.2
0.3
0.1
0.1
0
100 200 300 400 100 200 300 400
Re Re
Inlet thermal resistance Outlet thermal resistance
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38. Numerical Validation PDF (3)
• 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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39. Numerical Validation PDF (4)
Roughened (ribbed) microchannel:
• Comparison of numerical results with experimental
(Hao et al. 2006) and theoretical results (London and Shah 1978).
1.75
1.25 Present model
0.75 Reference [Theoritical]
0.25
f
f=65.3/Re
1000 3000
Re
Ribbed microchannel
dh=154 μm
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40. Numerical Validation PDF (5)
Roughened (ribbed) microchannel:
•Comparison of numerical results with experimental
(Hao et al. 2006) and theoretical results (London and Shah 1978).
0.6
0.4
0.2
f
f=61.3/Re
Present model
Reference [Theoritical]
500 1500 2500
Re
Ribbed microchannel
dh=191 μm
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41. Numerical Validation EOF
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42. Numerical Validation EOF
• Validation of present model for pressure driven flow
(PDF) and electroosmotic flow (EOF)
25
Arulanandam and Li (2000) Shah and London (1978) PDF
Volume flow rate (l min )
-1
Morini et al. (2006) Present model PDF
5E-05 Present model EOF 20
Morini (1999) slug flow
Present model EOF
15
Nufd
3E-05
10
5
1E-05
0
5E-05 0.0001 0.00015 0.0002 0.00025 0.15 0.2 0.25
dh (m) θ
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43. Microchannel Analyses PDF
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44. Simulation Results PDF (1)
Rectangular microchannel heat sink:
•Variation of thermal resistance with design variables
at constant pumping power and uniform heat flux.
0.28
0.26 φ = 0.4 θ = 0.4
φ = 0.6 0.26 θ = 0.6
φ = 0.8 θ = 0.8
0.24
φ = 1.0 0.24 θ = 1.0
Rth (oC/W)
Rth (oC/W)
0.22 θ = wc / hc 0.22
0.2 φ = ww / hc 0.2
0.18 0.18
0.4 0.5 0.6 0.7 0.8 0.9 1 0.4 0.5 0.6 0.7 0.8 0.9 1
θ φ
Variation of thermal resistance Variation of thermal resistance
with channel width with fin width
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45. Simulation Results PDF (2)
Rectangular microchannel heat sink:
•Temperature distribution for rectangular microchannel
heat sink.
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46. Simulation Results PDF (3)
Trapezoidal microchannel heat sink: variation of thermal resistance
with design variables at constant pumping power.
0.32
η = 0.5 η = 0.75
0.34 φ = 0.02 φ = 0.02
φ = 0.06 φ = 0.06
φ = 0.1 0.28 φ = 0.1
0.3
Rth ( C/W)
Rth ( C/W)
0.24
o
o
0.26
0.22 0.2
0.18
0.16
0.1 0.15 0.2 0.25 0.1 0.15 0.2 0.25
θ θ
0.26 η = 1.0
φ = 0.02
θ = wc / hc
φ = 0.06
0.24 φ = 0.1
Rth ( C/W)
φ = ww / hc
0.22
o
0.2
0.18
η = wb / wc
0.16
0.1 0.15 0.2 0.25
θ
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47. Simulation Results PDF (4)
Roughened (ribbed)
microchannel heat sink
Smooth microchannel
y
at = 0.5
ly
α 0.4, β 2.0, γ 0.112
= =
α = hr / wc
β = wr / hr Temperature distribution
γ = wc / pr
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48. Simulation Results PDF (5)
Smooth microchannel Ribbed microchannel
Temperature distribution
= 0.4, β 2.0
α =
and γ = 0.112
1 2
x x
= 0.5 = 0.5156
lx lx 1 2
x
= 0.5
lx
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49. Simulation Results PDF (6)
Rough (ribbed) 1
microchannel heat sink
1 2 3 4
2
x x 3
= 0.5123 = 0.5156
lx lx
x x
= 0.5189 = 0.5325 4
lx lx
Vorticity
distribution
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50. Simulation Results PDF (7)
Rough (ribbed) microchannel heat sink:
• Thermal resistance characteristics with mass flow rate and
pumping power.
= 0.3, and γ 0.113
α =
0.2 0.2
0.6
Thermal resistance (K/W)
Thermal resistance (K/W)
β=0.0
β=0.0
Pumping power (W)
β=0.5
β=0.5
0.4
0.15 0.15
0.2
0.1 0.1
0
2E-05 4E-05 6E-05 0.1 0.3 0.5
Mass flow rate (kg/s) Pumping power (W)
= h= wr / hr and γ wc / pr
α r / wc , β =
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51. Microchannel Analyses EOF
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52. Results of Simulation (2)
• Variation of flow-rate and thermal resistance with source
pressure-drop and electric potential in PDF and EOF,
respectively.
Pressure drop (kPa) Pressure drop (kPa)
10 30 50 10 20 30 40 50 60
3.5E-08 0.45
2.5
Flow rate (m /s) (EOF)
Flow rate (m /s) (PDF)
PDF PDF
Rth (K/W) (EOF)
Rth (K/W) (PDF)
3.5E-09 EOF EOF
2
2.5E-08 0.35
3
2.5E-09 3 1.5
1.5E-08 0.25
1.5E-09 1
0.5 0.15
5E-09
5E-10
5 10 15 20 5 10 15 20
Electric potential (kV) Electric potential (kV)
= 0.175, ww / hc 0.075 and hc 400 µ m
wc / hc = =
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53. Results of Simulation (3)
• Variation of flow-rate and thermal resistance with zeta
potential in EOF.
3.5E-09 2.5
5 kV
5 kV
10 kV
10 kV
15 kV
15 kV
Flow rate (m3/s)
2.5E-09
Rth (K/W)
1.5
1.5E-09
5E-10 0.5
0.1 0.125 0.15 0.175 0.2 0.1 0.125 0.15 0.175 0.2
Zeta potential (V) Zeta potential (V)
= 0.175, ww / hc 0.075 and hc 400 µ m
wc / hc = =
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54. Results of Simulation (4)
• Velocity profiles for PDF, EOF and combined flow
(PDF+EOF).
1 mixed (PDF+EOF) 1
EOF
PDF
0.8 0.8
u (ms )
u (ms )
-1
-1
0.6 0.6
mixed (PDF+EOF)
EOF
0.4 0.4 PDF
0.2 0.2
0 0
0 0.1 0.2 0.3 0.4 0.5 0 0.25 0.5 0.75 1
y/wc z/hc
= 0.175, ww / hc 0.075 and hc 400 µ m
wc / hc = =
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55. Results of Simulation (5)
• Temperature profiles for PDF, EOF and combined flow
(PDF+EOF). 30 mixed (PDF+EOF)
EOF
PDF
T-Ti (K)
20
10
0
0 0.25 0.5 0.75 1
x/lx
24 24
mixed (PDF+EOF) mixed (PDF+EOF)
EOF EOF
PDF PDF
18 18
T-Ti (K)
T-Ti (K)
12 12
6
6
0 0.1 0.2 0.3 0.4 0.5 0 0.25 0.5 0.75 1
y/wc z/hc
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56. Results of Simulation (6)
• Variation of flow-rate and thermal resistance with electric
potential in combined flow (PDF+EOF).
10 kPa 10 kPa
1.5E-08 15 kPa 0.26 15 kPa
20 kPa 20 kPa
Flow rate (m3/s)
1.25E-08
Rth (K/W)
0.22
1E-08
7.5E-09 0.18
0 2 4 6 8 10 0 2 4 6 8 10
Electric Potential (kV) Electric Potential (kV)
= 0.175, ww / hc 0.075 and hc 400 µ m
wc / hc = =
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57. Results of Simulation (7)
• Equivalent pressure-head and flow-rate for combined flow
(PDF+EOF) at electric potential of 10kV.
Equivalent preesure head (kPa)
24
Equivalent pressure head
Flow rate 1.2E-08
20
Flow rate (m /s)
3
16
8E-09
12
8
4E-09
4
0 5 10 15 20
Pressure drop (kPa)
= 0.175, ww / hc 0.075 and hc 400 µ m
wc / hc = =
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58. Simulation Results EOF (4)
• Variation of thermal resistance with design variables for
PDF at dp=15kPa and for combined flow (PDF+EOF)
at dp=15kPa & EF=10kV/cm.
θ = 0.1 θ = 0.1
0.5
θ = 0.15 θ = 0.15
θ = 0.2 0.3 θ = 0.2
0.4 θ = 0.25 θ = 0.25
Rth (K/W)
Rth (K/W)
0.3
0.2
0.2
0.1 0.1
0.04 0.06 0.08 0.1 0.04 0.06 0.08 0.1
φ φ
= wc / hc and φ ww / hc
θ =
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59. Optimization PDF
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60. Single Objective Optimization PDF (1)
Smooth rectangular MCHS:
• Comparison of optimum thermal resistance
(using Kriging model) with a reference case.
• 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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61. Single Objective Optimization PDF (2)
Smooth rectangular MCHS:
• Temperature distribution for reference and optimized
geometry.
Tuckerman and Pease case-1 Optimized
(1981)
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62. Single Objective Optimization PDF (3)
Smooth rectangular MCHS:
• Temperature distribution for reference and optimized
geometry.
Tuckerman and Pease (1981) Optimized
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63. Single Objective Optimization PDF (4)
Smooth rectangular MCHS:
• Sensitivity of objective function with design variables.
θ
0.003
φ
(Rth-Rth,opt)/Rth,opt
0.002
θ = wc / hc
φ = ww / hc
0.001
0
-10 -5 0 5 10
Deviation from optimal point (%)
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64. Single Objective Optimization PDF (5)
Smooth trapezoidal MCHS:
• Optimum thermal resistance (using RBNN model)
at uniform heat flux and constant 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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65. Single Objective Optimization PDF (6)
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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66. Multi-objective Optimization (1)
Smooth rectangular MCHS:
• Multiobjective optimization using MOEA and RSA.
• Pareto optimal front.
0.16
NSGA-II
Thermal Resistance (K/W)
A Hybrid method
0.14 Clusters
POC
0.12
B
0.1
C
0.08
0 0.2 0.4 0.6 0.8
Pumping Power (W)
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67. Multi-objective Optimization (2)
Smooth rectangular MCHS:
•Pareto optimal solutions grouped by k-means clustering.
Design variables
S. No. Rth (K/W) P (W)
θ φ
1(A) 0.180 0.080 0.144 0.064
2 0.157 0.076 0.128 0.173
3(B) 0.130 0.071 0.110 0.366
4 0.110 0.068 0.096 0.563
5(C) 0.100 0.061 0.090 0.677
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68. Multi-objective Optimization (3)
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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69. Multi-objective Optimization (5)
Trapezoidal MCHS:
• Sensitivity of objective functions to design variables over
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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70. Multi-objective Optimization (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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71. Multi-objective Optimization (5)
Roughened (ribbed) MCHS:
• Sensitivity of objective functions to design variables over
Pareto optimal front.
1 1
0.8
Design variables
0.8
Design variables
0.6 0.6
0.4 0.4
α α
0.2 0.2
β β
γ γ
0 0
0.175 0.18 0.185 0.04 0.06 0.08 0.1 0.12
Thermal resisteance (K/W) Pumping power (W)
= h= wr / hr and γ wc / pr
α r / wc , β =
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72. Optimization EOF
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73. Single Objective Optimization EOF (1)
• 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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74. Multi-objective Optimization (1)
• Pareto-optimal front with representative cluster points
at dp=15kPa and EF=10kV.
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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75. Multi-objective Optimization (2)
• Distribution of design variables along the Pareto-optimal
front at the selected cluster points.
θ 0.8 θ
0.8 E A
A φ (PDF+EOF) φ (PDF+EOF)
Design variables
Design variables
0.4 0.4
B B
D
D
C
C E
0
0
0.01 0.02 0.03
0.15 0.2 0.25
P (W)
Rth (K/W)
= wc / hc and φ ww / hc
θ =
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76. Summery and Conclusions
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77. Summery and Conclusions (1)
• A three-dimensional smooth rectangular and trapezoidal
microchannel and roughened (ribbed) MCHSs have been
studied and optimized for minimum thermal resistance and
pumping power at constant heat flux.
• Smooth MCHS: thermal resistance is found to be sensitive
to all design variables though it is higher sensitive to
channel width-to-depth and channel top-to-bottom width
ratio than the fin width-to-depth ratio.
• Ribbed MCHS: objective functions were found to be
sensitive to all design variables though they are higher
sensitive to rib width-to-height ratio than the rib height-to-
width of channel and channel width-to-pitch of the rib ratios.
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78. Summery and Conclusions (2)
• Ribbed MCHS: the application of the rib-structures in the
MCHSs strongly depends upon the design conditions and
available pumping source.
• Ribbed MCHS: with increase of mass flow rate rib-structures
decrease thermal resistance at higher pumping power than the
smooth microchannel.
• Ribbed MCHS: with increase of pumping power the
difference of thermal resistance reduces and eventually
ribbed microchannel offers lower thermal resistance than the
smooth microchannel.
• Application of surrogate models was explored to the
optimization of micro-fluid systems. Surrogate predictions
were found reasonably close to numerical values.
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79. Conclusions
• Surrogate-based optimization techniques can be utilized to
microfluidic systems to effectively reduce the optimization
time and expenses.
• 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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80. Thanks for your patient listening
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