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- 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 Inha University 2
- 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. Inha University 3
- 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. Inha University 4
- 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. Inha University 5
- 6. Model Definition Inha University 6
- 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 Inha University 7
- 8. Boundary Conditions Outflow Symmetric boundary Adiabatic boundaries Symmetric boundaries Silicon substrate q Heat flux Inflow Computational domain Half pitch of the microchannel Inha University 8
- 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 Inha University 9
- 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 Inha University 10
- 11. Numerical Scheme Inha University 11
- 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. Inha University 12
- 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. Inha University 13
- 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 Inha University 14
- 15. Models for Optimization Inha University 15
- 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. Inha University 16
- 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. Inha University 17
- 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. Inha University 18
- 19. Optimization Procedure Inha University 19
- 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 Inha University 20
- 21. Multiobjective Optimization Technique Objective Functions Rth and P Inha University 21
- 22. Surrogate Models Inha University 22
- 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 Inha University 23
- 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 Inha University 24
- 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 Inha University 25
- 26. Numerical Validation Inha University 26
- 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 Inha University 27
- 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 Inha University 28
- 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 Inha University 29
- 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 Inha University 30
- 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 Inha University 31
- 32. Microchannel Analyses Inha University 32
- 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 Inha University 33
- 34. Results of Optimization (2) Rectangular microchannel heat sink: •Temperature distribution for rectangular microchannel heat sink. Inha University 34
- 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 Inha University 35
- 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 Inha University 36
- 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 Inha University 37
- 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 Inha University 38
- 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) Inha University 39
- 40. Optimization Inha University 40
- 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 Inha University 41
- 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 Inha University 42
- 43. Single Objective Optimization (3) Smooth rectangular microchannel heat sink: • Temperature distribution for reference and optimized geometry. reference optimized Inha University 43
- 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 (%) Inha University 44
- 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 Inha University 45
- 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 Inha University 46
- 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) Inha University 47
- 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 Inha University 48
- 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) Inha University 49
- 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) Inha University 50
- 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) Inha University 51
- 52. Summery and Conclusions Inha University 52
- 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. Inha University 53
- 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. Inha University 54
- 55. Thanks for your patient listening Inha University 55

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