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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 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 Inha University 2
  • 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. Inha University 3
  • 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 Inha University 4
  • 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 Inha University 5
  • 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. Inha University 6
  • 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. Inha University 7
  • 8. Microchannel Heat Sink Designs Inha University 8
  • 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 Inha University 9
  • 10. Boundary Conditions Outflow Symmetric boundary Adiabatic boundaries Symmetric boundaries Silicon substrate q Heat flux Inflow Computational domain Half pitch of the microchannel Inha University 10
  • 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 Inha University 11
  • 12. Numerical Scheme Pressure-driven Flow (PDF) Electroosmotic Flow (EOF) Inha University 12
  • 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. Inha University 13
  • 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 Inha University 14
  • 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 ∇ Inha University 15
  • 16. Optimization Procedure Inha University 16
  • 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 Inha University 17
  • 18. Multi-objective Optimization Technique Objective Functions Rth and P Inha University 18
  • 19. Designs for Optimization Inha University 19
  • 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 Inha University 20
  • 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). Inha University 21
  • 22. Numerical Validation Inha University 22
  • 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 Inha University 23
  • 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 Inha University 24
  • 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 Inha University 25
  • 26. Microchannel Heat Sink Analysis Inha University 26
  • 27. Simulation Results PDF (1) Rectangular MCHS: •Variation of thermal resistance with design variables at constant pumping power and 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 27
  • 28. Simulation Results PDF (2) Trapezoidal MCHS: variation of thermal resistance with design variables at constant pumping power and heat flux. 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) hc = 370 µ m 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 28
  • 29. Simulation Results PDF (3) Roughened (ribbed) MCHS: • 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 29
  • 30. Simulation Results EOF • 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 30
  • 31. Optimization Results Pressure-driven Flow (PDF) Inha University 31
  • 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 Inha University 32
  • 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 Inha University 33
  • 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 Inha University 34
  • 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) Inha University 35
  • 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) Inha University 36
  • 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 Inha University 37
  • 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) Inha University 38
  • 39. Optimization Results Electroosmotic Flow (EOF) Inha University 39
  • 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 Inha University 40
  • 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) Inha University 41
  • 42. Conclusions Inha University 42
  • 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. Inha University 43
  • 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). Inha University 44
  • 45. Thanks for your patient listening Inha University 45
  • 46. Comments and Suggestions Inha University 46
  • 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. Inha University 47
  • 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 Inha University 48
  • 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 Inha University 49
  • 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. Inha University 50
  • 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 Inha University 51
  • 52. Comments and Suggestions Selected Title Numerical Analysis and Design Optimization of Pressure- and Electroosmotically-Driven Liquid Flow Microchannel Heat sinks Inha University 52