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- 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 Inha University 2
- 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 Inha University 3
- 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. Inha University 4
- 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 Inha University 5
- 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 Inha University 6
- 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. Inha University 7
- 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). Inha University 8
- 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. Inha University 9
- 10. Model Definition Inha University 10
- 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 Inha University 11
- 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 Inha University 12
- 13. Boundary Conditions Outflow Symmetric boundary Adiabatic boundaries Symmetric boundaries Silicon substrate q Heat flux Inflow Computational domain Half pitch of the microchannel Inha University 13
- 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 Inha University 14
- 15. Numerical Scheme Pressure-driven Flow (PDF) Inha University 15
- 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. Inha University 16
- 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. Inha University 17
- 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 Inha University 18
- 19. Numerical Scheme Electroosmotic flow (EOF) and Combined Flow (PDF+EOF) Inha University 19
- 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 Inha University 20
- 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 Inha University 21
- 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. Inha University 22
- 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 ∇ Inha University 23
- 24. Models for Optimization Inha University 24
- 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. Inha University 25
- 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. Inha University 26
- 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. Inha University 27
- 28. Optimization Procedure Inha University 28
- 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 Inha University 29
- 30. Multi-objective Optimization Technique Objective Functions Rth and P Inha University 30
- 31. Surrogate Models Inha University 31
- 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 Inha University 32
- 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 Inha University 33
- 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 Inha University 34
- 35. Numerical Validation PDF Inha University 35
- 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 Inha University 36
- 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 Inha University 37
- 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 Inha University 38
- 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 Inha University 39
- 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 Inha University 40
- 41. Numerical Validation EOF Inha University 41
- 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 Inha University 42
- 43. Microchannel Analyses PDF Inha University 43
- 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 Inha University 44
- 45. Simulation Results PDF (2) Rectangular microchannel heat sink: •Temperature distribution for rectangular microchannel heat sink. Inha University 45
- 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 Inha University 46
- 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 Inha University 47
- 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 Inha University 48
- 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 Inha University 49
- 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 = Inha University 50
- 51. Microchannel Analyses EOF Inha University 51
- 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 = = Inha University 52
- 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 = = Inha University 53
- 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 = = Inha University 54
- 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 Inha University 55
- 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 = = Inha University 56
- 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 = = Inha University 57
- 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 = Inha University 58
- 59. Optimization PDF Inha University 59
- 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 Inha University 60
- 61. Single Objective Optimization PDF (2) Smooth rectangular MCHS: • Temperature distribution for reference and optimized geometry. Tuckerman and Pease case-1 Optimized (1981) Inha University 61
- 62. Single Objective Optimization PDF (3) Smooth rectangular MCHS: • Temperature distribution for reference and optimized geometry. Tuckerman and Pease (1981) Optimized Inha University 62
- 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 (%) Inha University 63
- 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 Inha University 64
- 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 Inha University 65
- 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) Inha University 66
- 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 Inha University 67
- 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) Inha University 68
- 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 Inha University 69
- 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) Inha University 70
- 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 = Inha University 71
- 72. Optimization EOF Inha University 72
- 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 Inha University 73
- 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) Inha University 74
- 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 = Inha University 75
- 76. Summery and Conclusions Inha University 76
- 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. Inha University 77
- 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. Inha University 78
- 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). Inha University 79
- 80. Thanks for your patient listening Inha University 80

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