Abstract
The topology optimization (TO) method is developed and applied to 3D heat sink design optimization using the finite element method (FEM). To go from theory to practical application of optimized heat sink designs, the impact of the ratio between fin height () and substrate thickness () on the performance of heat sinks was investigated, studying the critical role of geometric parameters in heat dissipation performance, focusing on optimizing the internal fluid channels to enhance the overall hydraulic and thermal efficiencies under various operating conditions. Optimal flow conditions vary across TO designs; notably, structures with near-equal () and () ratios demonstrated superior energy and fluid flow overall performances. At high Reynolds numbers, the optimized heat sink designs showed an enhancement in the overall performance up to 41.2%, showcasing the effectiveness of the present TO method. The new 3D optimal designs can be applied to different applications such as the cooling of CPU, GPU, and different electronic chips.
References
1.
Tang
, K.
, Lin
, G. P.
, Guo
, Y. D.
, Huang
, J. Y.
, Zhang
, H. X.
, and Miao
, J. Y.
, 2023
, “Simulation and Optimization of Thermal Performance in Diverging/Converging Manifold Microchannel Heat Sink
,” Int. J. Heat Mass Transfer
, 200
, p. 123495
.2.
Moore
, A. L.
, and Shi
, L.
, 2014
, “Emerging Challenges and Materials for Thermal Management of Electronics
,” Mater. Today
, 17
(4
), pp. 163
–174
. 3.
Rathore
, V.
, Lokhande
, A. A.
, Mane
, Y. G.
, and Lele
, M. M.
, 2023
, Heat Transfer Enhancement of Fin and Tube Heat Exchanger Using Ribs
, Springer
, pp. 399
–407
.4.
Ali
, E.
, Tamang
, S.
, Park
, J.
, Choi
, J.
, Choi
, J.
, Park
, C.
, and Park
, H.
, 2024
, “A Novel Spiral Grooved Cooling Path Heat Sink for the Cooling of High Voltage Direct Current Devices
,” Int. J. Therm. Sci.
, 195
, p. 108665
. 5.
Gore
, S. S.
, and Dhoble
, A. J. M. T. P.
, 2023
, “Server Processor Heat Sink Analysis and Modifications to Improve Its Thermal Performance
,” Mater. Today: Proc.
, 82
, pp. 208
–216
. S2214-7853(23)00170-0],[10.1016/j.matpr.2023.01.1186.
Durgam
, S.
, Ghodake
, B.
, and Mohite
, S.
, 2022
, “Numerical Investigation on Heat Sink Material for Temperature Control of Electronics
,” J. Phys.: Conf. Ser.
, 2312
(1
), p. 012016
. 7.
Kunjir
, C.
, and Gawali
, S.
, 2023
, “Numerical Analysis and Optimization Flow Around Array of Heated Semi-circular Fins
,” AIP Conf. Proc.
, 2427
, p. 020072
. 8.
Tuckerman
, D. B.
, and Pease
, R. F. W.
, 1981
, “High-Performance Heat Sinking for Vlsi
,” Electron Device Lett.
, 2
(5
), pp. 126
–129
. 9.
Pan
, H.
, Liu
, X.
, Yang
, Q.
, Xu
, H.
, and Xu
, D.
, 2023
, “Three-Dimensional Lattice Boltzmann Study on Structure Optimization and Heat Dissipation Performance of Pin-Fin Heat Sink Integrated With Phase Change Material
,” J. Energy Storage
, 71
, p. 108233
. 10.
Piancastelli
, L.
, Sportiello
, L.
, Pezzuti
, E.
, and Cassani
, S.
, 2019
, “Study and Optimization of Advanced Heat Sinks for Processors
,” J. Eng. Appl. Sci.
, 14
(5
), pp. 1082
–1088
.11.
Xie
, W.
, Xia
, Q.
, Yu
, Q.
, and Li
, Y.
, 2023
, “An Effective Phase Field Method for Topology Optimization Without the Curvature Effects
,” Comput. Math. Appl.
, 146
, pp. 200
–212
. 12.
Bendsoe
, M. P.
, and Kikuchi
, N.
, 1988
, “Generating Optimal Topologies in Structural Design Using a Homogenization Method
,” Comput. Methods Appl. Mech. Eng.
, 71
(2
), pp. 197
–224
. 13.
Yang
, C.
, Wang
, D.
, Ali
, S.
, Wang
, G.
, and Dbouk
, T.
, 2025
, “Topology Optimization of Rectangular Parallel Plate Heat Exchanger Unit
,” Int. J. Therm. Sci.
, 208
, p. 109503
. 14.
Guest
, J. K.
, and Prevost
, J. H.
, 2006
, “Topology Optimization of Creeping Fluid Flows Using a Darcy-Stokes Finite Element
,” Int. J. Numer. Methods Eng.
, 66
(3
), pp. 461
–484
. 15.
Wang
, C.
, Fang
, L.
, Wang
, X.
, Zhou
, H.
, and Guo
, X.
, 2024
, “Topology Optimization of Steady Navier-Stokes Flow Using Moving Morphable Void Method
,” Comput. Math. Appl.
, 161
, pp. 212
–224
. 16.
Borrvall
, T.
, and Petersson
, J.
, 2003
, “Topology Optimization of Fluids in Stokes Flow
,” Int. J. Numer. Methods Fluids
, 41
(1
), pp. 77
–107
. 17.
Olesen
, L. H.
, Okkels
, F.
, and Bruus
, H.
, 2006
, “A High-Level Programming-Language Implementation of Topology Optimization Applied to Steady-State Navier-Stokes Flow
,” Int. J. Numer. Methods Eng.
, 65
(7
), pp. 975
–1001
. 18.
Gersborg-Hansen
, A.
, Sigmund
, O.
, and Haber
, R. B.
, 2005
, “Topology Optimization of Channel Flow Problems
,” Struct. Multidiscipl. Optim.
, 30
(3
), pp. 181
–192
. 19.
Evgrafov
, A.
, 2006
, “Topology Optimization of Slightly Compressible Fluids
,” Zamm Z. Angew. Math. Mech.
, 86
(1
), pp. 46
–62
. 20.
Pingen
, G.
, and Maute
, K.
, 2010
, “Optimal Design for Non-Newtonian Flows Using a Topology Optimization Approach
,” Comput. Math. Appl.
, 59
(7
), pp. 2340
–2350
. 21.
Yoon
, G. H.
, 2016
, “Topology Optimization for Turbulent Flow With Spalart-Allmaras Model
,” Comput. Methods Appl. Mech. Eng.
, 303
, pp. 288
–311
. 22.
Dilgen
, C. B.
, Dilgen
, S. B.
, Fuhrman
, D. R.
, Sigmund
, O.
, and Lazarov
, B. S.
, 2018
, “Topology Optimization of Turbulent Flows
,” Comput. Methods Appl. Mech. Eng.
, 331
, pp. 363
–393
. 23.
Gersborg-Hansen
, A.
, Bendsoe
, M. P.
, and Sigmund
, O.
, 2006
, “Topology Optimization of Heat Conduction Problems Using the Finite Volume Method
,” Struct. Multidiscipl. Optim.
, 31
(4
), pp. 251
–259
. 24.
Bruns
, T. E.
, 2007
, “Topology Optimization of Convection-Dominated, Steady-State Heat Transfer Problems
,” Int. J. Heat Mass Transfer
, 50
(15–16
), pp. 2859
–2873
. 25.
Luo
, J.-W.
, Chen
, L.
, Wang
, Z.
, and Tao
, W.
, 2022
, “Topology Optimization of Thermal Cloak Using the Adjoint Lattice Boltzmann Method and the Level-Set Method
,” Appl. Therm. Eng.
, 216
, p. 119103
.26.
Dbouk
, T.
, 2017
, “A Review About the Engineering Design of Optimal Heat Transfer Systems Using Topology Optimization
,” Appl. Therm. Eng.
, 112
, pp. 841
–854
. 27.
Zeng
, S.
, and Lee
, P. S.
, 2019
, “Topology Optimization of Liquid-Cooled Microchannel Heat Sinks: An Experimental and Numerical Study
,” Int. J. Heat Mass Transfer
, 142
, p. 118401
. 28.
Zeng
, T.
, Wang
, H.
, Yang
, M.
, and Alexandersen
, J.
, 2020
, “Topology Optimization of Heat Sinks for Instantaneous Chip Cooling Using a Transient Pseudo-3D Thermofluid Model
,” Int. J. Heat Mass Transfer
, 154
, p. 119681
. 29.
Dede
, E. M.
, 2010
, “Multiphysics Optimization, Synthesis, and Application of Jet Impingement Target Surfaces
,” 12th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems
, Las Vegas, NV
, June 2–5
, pp. 1
–7
.30.
Dede
, E. M.
, 2012
, “Optimization and Design of a Multipass Branching Microchannel Heat Sink for Electronics Cooling
,” ASME J. Electron. Packag.
, 134
(4
), p. 041001
. 31.
Koga
, A. A.
, Lopes
, E. C. C.
, Villa Nova
, H. F.
, de Lima
, C. R.
, and Nelli Silva
, E. C.
, 2013
, “Development of Heat Sink Device by Using Topology Optimization
,” Int. J. Heat Mass Transfer
, 64
, pp. 759
–772
. 32.
Lv
, Y.
, and Liu
, S.
, 2018
, “Topology Optimization and Heat Dissipation Performance Analysis of a Micro-channel Heat Sink
,” Meccanica
, 53
(15
), pp. 3693
–3708
. 33.
Haertel
, J. H. K.
, Engelbrecht
, K.
, Lazarov
, B. S.
, and Sigmund
, O.
, 2018
, “Topology Optimization of a Pseudo 3D Thermofluid Heat Sink Model
,” Int. J. Heat Mass Transfer
, 121
, pp. 1073
–1088
. 34.
Hassanzadeh
, A.
, Moradi
, S.
, and Burton
, H. V.
, 2024
, “Performance-Based Design Optimization of Structures: State-of-the-Art Review
,” J. Struct. Eng.
, 150
(8
), p. 03124001
. 35.
He
, W.
, Wang
, S.
, Li
, Y.
, and Zhao
, Y.
, 2016
, “Structural Size Optimization on an Exhaust Exchanger Based on the Fluid Heat Transfer and Flow Resistance Characteristics Applied to an Automotive Thermoelectric Generator
,” Energy Convers. Manage.
, 129
, pp. 240
–249
. 36.
Sigmund
, O.
, and Maute
, K.
, 2013
, “Topology Optimization Approaches: A Comparative Review
,” Struct. Multidiscipl. Optim.
, 48
(6
), pp. 1031
–1055
. 37.
Li
, H.
, Kondoh
, T.
, Jolivet
, P.
, Furuta
, K.
, Yamada
, T.
, Zhu
, B.
, Zhang
, H.
, Izui
, K.
, and Nishiwaki
, S.
, 2022
, “Optimum Design and Thermal Modeling for 2D and 3D Natural Convection Problems Incorporating Level Set-Based Topology Optimization With Body-Fitted Mesh
,” Int. J. Numer. Methods Eng.
, 123
(9
), pp. 1954
–1990
. 38.
Liu
, A.
, Wang
, G.
, Wang
, D.
, Peng
, X.
, and Yuan
, H.
, 2021
, “Study on the Thermal and Hydraulic Performance of Fin-and-Tube Heat Exchanger Based on Topology Optimization
,” Appl. Therm. Eng.
, 197
, p. 117380
. 39.
Vorayos
, N.
, and Kiatsiriroat
, T.
, 2010
, “Thermal Characteristics of Louvered Fins With a Low-Reynolds Number Flow
,” J. Mech. Sci. Technol.
, 24
, pp. 845
–850
. 40.
Yoon
, G. H.
, 2010
, “Topological Design of Heat Dissipating Structure With Forced Convective Heat Transfer
,” J. Mech. Sci. Technol.
, 24
(6
), pp. 1225
–1233
. 41.
Xu
, L.
, Li
, H.
, Ding
, X.
, Liu
, S.
, and IEEE
, 2017
, “Design of Microchannel Heat Sink Using Topology Optimization for High Power Modules Cooling
.”42.
Sato
, Y.
, Yaji
, K.
, Izui
, K.
, Yamada
, T.
, and Nishiwaki
, S.
, 2018
, “An Optimum Design Method for a Thermal-Fluid Device Incorporating Multiobjective Topology Optimization With an Adaptive Weighting Scheme
,” J. Mech. Des.
, 140
(3
), p. 031402
. 43.
Li
, H.
, Ding
, X.
, Meng
, F.
, Jing
, D.
, and Xiong
, M.
, 2019
, “Optimal Design and Thermal Modelling for Liquid-Cooled Heat Sink Based on Multi-objective Topology Optimization: An Experimental and Numerical Study
,” Int. J. Heat Mass Transfer
, 144
, p. 118638
. 44.
Zeng
, S.
, Kanargi
, B.
, and Lee
, P. S.
, 2018
, “Experimental and Numerical Investigation of a Mini Channel Forced Air Heat Sink Designed by Topology Optimization
,” Int. J. Heat Mass Transfer
, 121
, pp. 663
–679
. 45.
Qian
, X.
, and Dede
, E. M.
, 2016
, “Topology Optimization of a Coupled Thermal-Fluid System Under a Tangential Thermal Gradient Constraint
,” Struct. Multidiscipl. Optim.
, 54
(3
), pp. 531
–551
. 46.
Dede
, E. M.
, Joshi
, S. N.
, and Zhou
, F.
, 2015
, “Topology Optimization, Additive Layer Manufacturing, and Experimental Testing of an Air-Cooled Heat Sink
,” J. Mech. Des.
, 137
(11
), p. 111403
. 47.
Alexandersen
, J.
, Sigmund
, O.
, and Aage
, N.
, 2016
, “Large Scale Three-Dimensional Topology Optimisation of Heat Sinks Cooled by Natural Convection
,” Int. J. Heat Mass Transfer
, 100
, pp. 876
–891
. 48.
Sigmund
, O.
, and Petersson
, J.
, 1998
, “Numerical Instabilities in Topology Optimization: A Survey on Procedures Dealing With Checkerboards, Mesh-Dependencies and Local Minima
,” Struct. Optim.
, 16
, pp. 68
–75
. 49.
Lazarov
, B. S.
, and Sigmund
, O.
, 2011
, “Filters in Topology Optimization Based on Helmholtz-Type Differential Equations
,” Int. J. Numer. Methods Eng.
, 86
(6
), pp. 765
–781
. 50.
Wang
, F.
, Lazarov
, B. S.
, and Sigmund
, O.
, 2011
, “On Projection Methods, Convergence and Robust Formulations in Topology Optimization
,” Struct. Multidiscipl. Optim.
, 43
, pp. 767
–784
. 51.
Xu
, S.
, Cai
, Y.
, and Cheng
, G.
, 2010
, “Volume Preserving Nonlinear Density Filter Based on Heaviside Functions
,” Struct. Multidiscipl. Optim.
, 41
, pp. 495
–505
. 52.
Kawamoto
, A.
, Matsumori
, T.
, Yamasaki
, S.
, Nomura
, T.
, Kondoh
, T.
, and Nishiwaki
, S.
, 2011
, “Heaviside Projection Based Topology Optimization by a PDE-Filtered Scalar Function
,” Struct. Multidiscipl. Optim.
, 44
, pp. 19
–24
. 53.
Wang
, G. H.
, Liu
, A. K.
, Dbouk
, T.
, Wang
, D. B.
, Peng
, X.
, and Ali
, A.
, 2022
, “Optimal Shape Design and Performance Investigation of Helically Coile D Tube Heat Exchanger Applying Mo-Sherpa
,” Int. J. Heat Mass Transfer
, 184
, p. 122256
.54.
Gao
, H.
, Zhang
, Y.
, Liu
, Y.
, Wang
, Y.
, Sun
, P.
, Ma
, Y.
, Gu
, Z.
, and Yu
, W.
, 2022
, “Numerical Simulation of Heat Transfer Performance of Different Heat Exchange Tubes in Heat Recovery Steam Generator
,” Process Saf. Environ. Prot.
, 163
, pp. 506
–512
. 55.
Hino
, T.
, Suzuki
, K.
, and Takagi
, Y.
, 2022
, “Modification of K- Turbulence Model for Ship Resistance Flow Predictions
,” J. Ocean Eng. Mar. Energy
, 8
(4
), pp. 527
–538
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