1. Fourth International Symposium on Fluid Machinery and Fluid Engineering
Nov. 24-27, 2008, Beijing, China
Microchannel Heat Sinking: Analysis and
Optimization
Afzal Husain and Kwang-Yong Kim*
Mechanical Engineering Department,
Inha University, Korea

2. Introduction
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3. Background: microchannel heat sink
• Microchannel heat sink has been used as an efficient
cooling device for electronics, avionics, and micro
refrigerators etc.
• Experimental studies have been carried out and analytical
and numerical models have been developed with certain
assumptions to understand the heat transfer and fluid flow
phenomena in the microchannel heat sink.
• The growing demand for higher heat dissipation and
miniaturization have directed to focused studies to efficiently
utilize the silicon material, space and to optimize the
microchannel heat sinking.
• Alternative designs had been applied to enhance the
performance of microchannel heat sink.
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4. Motivation
• The present study is motivated to utilize the potential of this
micro-electronic cooling technology to improve the
performance of the heat carrying system.
• The geometrical parameters of microchannel heat sink
which greatly affect the performance of the microchannel
need to study and optimize in the light of pumping power
and overall thermal resistance.
• The dimensions to be optimized must compliance to the
micro-fabrication processes available e.g., KOH wet etching,
anisotropic etching, LIGA and DRIE for economic design.
• Numerical methods in combination with the surrogate-based
optimization techniques can be useful to optimize the
microchannel heat sink economically.
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5. Objectives
• To find out the effects of design variables on thermal
performance of the micro-channel heat sink.
• To study and optimize the smooth and rough (ribbed)
microchannel heat sink.
• To apply surrogate-based optimization techniques to micro-
fluid systems to enhance thermal performance economically
under the flow and manufacturing constraints.
• Single and multiobjective optimization of microchannel heat
sink considering pumping power and thermal resistance as
performance objective functions.
• To find out sensitivity of objective functions to design
variables to suitably adjust the geometric parameter
insensitive to the heat sink performance.
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6. Model Definition
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7. Microchannel Heat Sink
A microchannel heat sink of 10mm ×10mm × 0.5mm is set to
study under uniform heat flux at the base to minimize overall
thermal resistance.
Microchannel heat sink Computational domain
Silicon substrate
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8. 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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9. Smooth Microchannel
• Formation of design variables.
Design variables
θ = Wc / H c
φ = Ww / H c
η = Wb / Wc
Silicon substrate
• For rectangular cross-section Wb = Wc
• For trapezoidal cross-section 0 < Wb < Wc
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10. Rough (Ribbed) Microchannel
• Formation of design variables.
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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11. Numerical Scheme
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12. Numerical Scheme (1)
• Silicon-based ribbed microchannel heat sink with deionized
ultra-filtered water (DIUF) as coolant.
• A steady, incompressible, and laminar flow simulation.
• Finite-volume analysis of three-dimensional Navier-Stokes
and energy equations.
• Conjugate heat transfer analysis through interface of silicon
and water.
• Unstructured hexahedral mesh.
• Finer mesh for fluid flow cross-section and courser in the
solid region.
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13. Numerical Scheme (2)
• An overall mesh-system of 401×61×16 was used for 50µm
half-pitch after carrying out grid independency test for
smooth microchannel.
• A 501×61×41 grid was used for 100µm pitch after carrying
out grid independency test for rough microchannel.
• A constant heat flux (100 W/cm2) at the bottom of the
microchannel heat sink.
• Thermal resistance and pumping power were calculated at
the DOE points.
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14. Numerical Scheme (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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15. Models for Optimization
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16. 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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17. 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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18. 3-Rough (Ribbed) Microchannel
Rough (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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19. Optimization Procedure
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20. 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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21. Multiobjective Optimization Technique
Objective Functions Rth and P
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22. Surrogate Models
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23. 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 : regression coefficients
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24. 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 - known function
Z(x) : localized deviation - realization of a
stochastic process
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25. 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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26. Numerical Validation
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27. Numerical Validation (1)
• Comparison of numerically simulated velocity profiles with
analytical data in two different directions for smooth
rectangular microchannel heat sink.
0.4 0.4
Shah and London [26] Shah and Lo
1 0.2
1 Present model 0.2 Present mod
0 0
0 0.25 0.5 0.75 1 0 0.25 0.5
y/ymax z/zmax
0.8 0.8
u/umax
u/umax
0.6 0.6
0.4 0.4
Shah and London Shah and London
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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28. Numerical Validation (2)
• Comparison of numerically simulated thermal resistances
with experimental results for smooth rectangular
microchannel heat sink.
0.4
0.6 Kawano et al.
Kawano et al.
0.3 Present model Present model
Rth,o (oCcm2/W)
Rth,i ( Ccm /W)
200 300 400
Re
2
0.4
0.2
o
0.2
0.1 0.6 Kawano et al. [4]
Present model
Rth,o (oCcm2/W)
0.4
0 0
100 200 300 400 100 0.2 200 300 400
Re Re
Inlet thermal resistance Outlet thermal resistance
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29. Numerical Validation (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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30. Numerical Validation (4)
Rough (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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31. Numerical Validation (5)
Rough (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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32. Microchannel Analyses
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33. Results of Simulation (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
0.22
0.2 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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34. Results of Optimization (2)
Rectangular microchannel heat sink:
•Temperature distribution for rectangular microchannel
heat sink.
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35. Results of Simulation (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
φ = 0.06
0.24 φ = 0.1
Rth ( C/W)
0.22
o
0.2
0.18
0.16
0.1 0.15 0.2 0.25
θ
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36. Results of Simulation (4)
Rough (ribbed)
microchannel heat sink
Smooth microchannel
= 0.4, β 2.0
α =
and γ = 0.112
y
at = 0.5 Temperature distribution
ly
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37. Results of Simulation (5)
Smooth microchannel Ribbed microchannel
Temperature distribution
= 0.4, β 2.0
α =
and γ = 0.112
x x
= 0.5 = 0.5156
lx lx
x x x
= 0.5 = 0.5 = 0.5156
lx lx lx
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38. Results of Simulation (6)
Rough (ribbed)
microchannel heat sink
x x
= 0.5123 = 0.5156
lx lx
x x
= 0.5189 = 0.5325
lx lx
Vorticity
distribution
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39. Results of Simulation (7)
Rough (ribbed) microchannel heat sink:
• Thermal resistance characteristics with mass flow rate and
pumping power.
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)
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40. Optimization
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41. Single Objective Optimization (1)
Smooth rectangular microchannel heat sink:
• Comparison of optimum thermal resistance
(using Kriging model) with a reference case.
• Two design variables consideration.
Models θ φ F
(CFD calculation)
Tuckerman and 0.175 0.138 0.214
Pease case-1
Present 0.174 0.053 0.171
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42. Single Objective Optimization (2)
Smooth rectangular microchannel heat sink:
• Temperature distribution for reference and optimized
geometry.
Reference KRG model
Tuckerman and Pease case-1 optimized
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43. Single Objective Optimization (3)
Smooth rectangular microchannel heat sink:
• Temperature distribution for reference and optimized
geometry.
reference optimized
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44. Single Objective Optimization (4)
Smooth rectangular microchannel heat sink:
• Sensitivity of objective function with design variables.
θ
0.003
φ
(Rth-Rth,opt)/Rth,opt
0.002
0.001
0
-10 -5 0 5 10
Deviation from optimal point (%)
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45. Single Objective Optimization (5)
Smooth trapezoidal microchannel heat sink:
• Optimum thermal resistance (using RBNN model)
at uniform heat flux and constant pumping power.
• Three design variables consideration.
Model θ φ η
F (Surrogate F (CFD
prediction) calculation)
Reference 0.154 0.116 1.000 0.1988 0.1922
(Kawano et al.)
Present 0.249 0.036 0.750 0.1708 0.1707
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46. Single Objective Optimization (6)
Smooth trapezoidal microchannel heat sink:
• 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 (%)
Reference (Kawano et al. 1998) Optimized
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47. Multiobjective Optimization (1)
Smooth rectangular microchannel heat sink:
• 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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48. Multiobjective Optimization (2)
Smooth rectangular microchannel heat sink:
•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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49. Multiobjective Optimization (3)
Smooth trapezoidal microchannel heat sink:
• Multiobjective optimization using MOEA and RSA.
• Pareto optimal front.
Thermal Resistance (K/W)
0.15 x
x
x
Hybrid method
7 Clusters
x
x
x
x
x
x
x
x
x
x
NSGA-II
xx
x
x
0.13 x
x
x
C
x
x
x
x
x
x
x
POC
x
x
x
x
x
x
x
0.11
x
x
x
x
x
x
x
x
x
B
x
x
x
x
x
x
x
x
xx
x
x x
x x
x
x x
0.09
x x
xx
x x
xx
A
x x
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
Pumping Power (W)
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50. Multiobjective Optimization (4)
Rough (ribbed) microchannel heat sink:
• 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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51. Multiobjective Optimization (5)
Rough (ribbed) microchannel heat sink:
• 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)
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52. Summery and Conclusions
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53. Summery and Conclusions (1)
• A three-dimensional smooth rectangular and trapezoidal
microchannel and rough (ribbed) microchannel heat sink
have been study and optimized for minimum thermal
resistance and pumping power at constant heat flux.
• Smooth microchannel heat sink: 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 microchannel heat sink: 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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54. Summery and Conclusions (2)
• Ribbed microchannel heat sink: the application of the rib-
structures in the microchannel heat sinks strongly depends
upon the design conditions and available pumping source.
• Ribbed microchannel heat sink: with increase of mass flow
rate rib-structures decrease thermal resistance at higher
pumping power than the smooth microchannel.
• Ribbed microchannel heat sink: 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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55. Thanks for your patient listening
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