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Constructal design progress for eight types of heat sinks

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Abstract

This review paper summarizes constructal design progress performed by the authors for eight types of heat sinks with ten performance indexes being taken as the optimization objectives, respectively, by combining the methods of theoretical analysis and numerical calculation. The eight types of heat sinks are uniform height rectangular fin heat sink, non-uniform height rectangular fin heat sink, inline cylindrical pin-fin heat sink (ICPHS), plate single-row pin fin heat sink (PSRPHS), plate inline pin fin heat sink (PIPHS), plate staggered pin fin heat sink (PSPHS), single-layered microchannel heat sink (SLMCHS) with rectangular cross sections and double-layered microchannel heat sink (DLMCHS) with rectangular cross sections, respectively. And the ten performance indexes are heat transfer rate maximization, maximum thermal resistance minimization, minimization of equivalent thermal resistance which is defined based on the entransy dissipation rate (equivalent thermal resistance for short), field synergy number maximization, entropy generation rate minimization, operation cost minimization, thermo-economic function value minimization, pressure drop minimization, enhanced heat transfer factor maximization and efficiency evaluation criterion number maximization, respectively. The optimal constructs of the eight types of heat sinks with different constraints and based on the different optimization objectives are compared with each other. The results indicated that the optimal constructs mostly are different based on different optimization objectives under the same boundary condition. The optimization objective should be suitable chosen based on the focus when the constructal design for one heat sink is performed. The results obtained herein have some important theoretical significances and application values, and can provide scientific bases and theoretical guidelines for the thermal design of real heat sinks and their applications.

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References

  1. Garimella S V, Fleischer A S, Murthy J Y, et al. Thermal challenges in next-generation electronic systems. IEEE Trans Comp Packag Technol, 2008, 31: 801–815

    Article  Google Scholar 

  2. Naphon P, Wiriyasart S, Wongwises S. Thermal cooling enhancement techniques for electronic components. Int Commun Heat Mass Transfer, 2015, 61: 140–145

    Article  Google Scholar 

  3. Bejan A. Street network theory of organization in nature. ATR, 1996, 30: 85–107

    Article  Google Scholar 

  4. Bejan A. Constructal-theory network of conducting paths for cooling a heat generating volume. Int J Heat Mass Transfer, 1997, 40: 799–816

    Article  MATH  Google Scholar 

  5. Bejan A, Merkx G W. Constructal Theory of Social Dynamics. New York: Springer, 2007

    Book  Google Scholar 

  6. Bejan A, Lorente S. Design with Constructal Theory. New York: Wiley, 2008

    Book  MATH  Google Scholar 

  7. Chen L G. Progress in study on constructal theory and its applications. Sci China Tech Sci, 2012, 55: 802–820

    Article  Google Scholar 

  8. Bejan A, Lorente S. Constructal law of design and evolution: Physics, biology, technology, and society. J Appl Phys, 2013, 113: 151301

    Article  Google Scholar 

  9. Bejan A. Constructal law: Optimization as design evolution. J Heat Transfer, 2015, 137: 061003

    Article  Google Scholar 

  10. Chen L G, Feng H J. Multi-objective Constructal Optimization for Flow and Heat and Mass Transfer Processes (in Chinese). Beijing: Science Press, 2016

    Google Scholar 

  11. Feng H, Chen L, Xie Z. Multi-disciplinary, multi-objective and multiscale constructal optimizations for heat and mass transfer processes performed in Naval University of Engineering, a review. Int J Heat Mass Transfer, 2017, 115: 86–98

    Article  Google Scholar 

  12. Razera A L, Errera M R, dos Santos E D, Isoldi L A, Rocha L A O. Constructal network of scientific publications, coauthorship and citations. Proc Roman Acad Ser A-Math Phys Tech Sci Inform Sci, 2018, 18: 105–110

    Google Scholar 

  13. Bejan A. Constructal law, twenty years after. Proc Roman Acad Ser AMath Phys Tech Sci Inform Sci, 2018, 18: 309–311

    Google Scholar 

  14. Miguel A F, Rocha L A O. Tree-Shaped Fluid Flow and Heat Transfer, New York: Springer, 2018

    Book  Google Scholar 

  15. Chen L, Feng H, Xie Z, et al. Progress of constructal theory in China over the past decade. Int J Heat Mass Transfer, 2019, 130: 393–419

    Article  Google Scholar 

  16. Guo Z Y, Zhu H Y, Liang X G. Entransy—A physical quantity describing heat transfer ability. Int J Heat Mass Transfer, 2007, 50: 2545–2556

    Article  MATH  Google Scholar 

  17. Guo Z, Cheng X, Xia Z. Least dissipation principle of heat transport potential capacity and its application in heat conduction optimization. Chin Sci Bull, 2003, 48: 406–410

    Article  Google Scholar 

  18. Chen L G. Progress in entransy theory and its applications. Chin Sci Bull, 2012, 57: 4404–4426

    Article  Google Scholar 

  19. Chen Q, Liang X G, Guo Z Y. Entransy theory for the optimization of heat transfer—A review and update. Int J Heat Mass Transfer, 2013, 63: 65–81

    Article  Google Scholar 

  20. Cheng X T, Liang X G. Entransy, entransy dissipation and entransy loss for analyses of heat transfer and heat-work conversion processes. JTST, 2013, 8: 337–352

    Article  Google Scholar 

  21. Chen L G. Progress in optimization of mass transfer processes based on mass entransy dissipation extremum principle. Sci China Tech Sci, 2014, 57: 2305–2327

    Article  Google Scholar 

  22. Chen L, Feng H, Xie Z. Generalized thermodynamic optimization for iron and steel production processes: Theoretical exploration and application cases. Entropy, 2016, 18: 353

    Article  Google Scholar 

  23. Kostic M M. Entransy concept and controversies: A critical perspective within elusive thermal landscape. Int J Heat Mass Transfer, 2017, 115: 340–346

    Article  Google Scholar 

  24. Chen L, Xiao Q, Feng H. Constructal optimizations for heat and mass transfers based on the entransy dissipation extremum principle, performed at the Naval University of Engineering: A review. Entropy, 2018, 20: 74

    Article  Google Scholar 

  25. Wei S, Chen L, Xie Z. Constructal heat conduction optimization: Progresses with entransy dissipation rate minimization. Thermal Sci Eng Prog, 2018, 7: 155–163

    Article  Google Scholar 

  26. Bejan A. Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes. J Appl Phys, 1996, 79: 1191–1218

    Article  Google Scholar 

  27. Chen L G, Wu C, Sun F R. Finite time thermodynamic optimization or entropy generation minimization of energy systems. J Non-Equilib Thermodyn, 1999, 24: 327–359

    MATH  Google Scholar 

  28. Ge Y, Chen L, Sun F. Progress in finite time thermodynamic studies for internal combustion engine cycles. Entropy, 2016, 18: 139

    Article  Google Scholar 

  29. Chen L G, Xia S J. Progresses in generalized thermodynamic dynamic-optimization of irreversible processes. Sci Sin-Tech, 2019, 49: 981–1022

    Article  Google Scholar 

  30. Guo Z Y, Li D Y, Wang B X. A novel concept for convective heat transfer enhancement. Int J Heat Mass Transfer, 1998, 41: 2221–2225

    Article  MathSciNet  MATH  Google Scholar 

  31. Guo Z. Mechanism and control of convective heat transfer. Chin Sci Bull, 2001, 46: 596–599

    Article  Google Scholar 

  32. Tao W Q, He Y L, Chen L. A comprehensive review and comparison on heatline concept and field synergy principle. Int J Heat Mass Transfer, 2019, 135: 436–459

    Article  Google Scholar 

  33. Webb R L, Scott M J. A parametric analysis of the performance of internally finned tubes for heat exchanger application. J Heat Transfer, 1980, 102: 38–43

    Article  Google Scholar 

  34. Webb R L. Performance evaluation criteria for use of enhanced heat transfer surfaces in heat exchanger design. Int J Heat Mass Transfer, 1981, 24: 715–726

    Article  Google Scholar 

  35. Li Z X, Guo Z Y. Field Synergy Theory of Convection Heat Transfer Optimization (in Chinese). Beijing: Science Press, 2010

    Google Scholar 

  36. Shuja S Z. Optimal fin geometry based on exergoeconomic analysis for a pin-fin array with application to electronics cooling. Exergy an Int J, 2002, 2: 248–258

    Article  Google Scholar 

  37. Yang A B. Performance analyses and multi-objective constructal optimizations for four kinds of heat sinks (in Chinese). Dissertation for Dcotoral Degree. Wuhan: Naval University of Engineering, 2017

    Google Scholar 

  38. Bejan A, Dan N. Constructal trees of convective fins. J Heat Transfer, 1999, 121: 675–682

    Article  Google Scholar 

  39. Alebrahim A, Bejan A. Constructal trees of circular fins for conductive and convective heat transfer. Int J Heat Mass Transfer, 1999, 42: 3585–3597

    Article  MATH  Google Scholar 

  40. Almogbel M, Bejan A. Cylindrical trees of pin fins. Int J Heat Mass Transfer, 2000, 43: 4285–4297

    Article  MATH  Google Scholar 

  41. Bejan A, Almogbel M. Constructal T-shaped fins. Int J Heat Mass Transfer, 2000, 43: 2101–2115

    Article  MATH  Google Scholar 

  42. Combelles L, Lorente S, Bejan A. Leaflike architecture for cooling a flat body. J Appl Phys, 2009, 106: 044906

    Article  Google Scholar 

  43. Lorenzini G, Biserni C, Correa R L, et al. Constructal design of T-shaped assemblies of fins cooling a cylindrical solid body. Int J Thermal Sci, 2014, 83: 96–103

    Article  Google Scholar 

  44. Lorenzini G, Rocha L A O. Constructal design of T-Y assembly of fins for an optimized heat removal. Int J Heat Mass Transfer, 2009, 52: 1458–1463

    Article  MATH  Google Scholar 

  45. Lorenzini G, Corrêa R L, Domingues dos Santos E, et al. Constructal design of complex assembly of fins. J Heat Transfer, 2011, 133: 081902

    Article  Google Scholar 

  46. Azoumah Y, Mazet N, Neveu P. Constructal network for heat and mass transfer in a solid-gas reactive porous medium. Int J Heat Mass Transfer, 2004, 47: 2961–2970

    Article  MATH  Google Scholar 

  47. Azoumah Y, Neveu P, Mazet N. Constructal design combined with entropy generation minimization for solid-gas reactors. Int J Thermal Sci, 2006, 45: 716–728

    Article  Google Scholar 

  48. Zhou S, Chen L, Sun F. Constructal entropy generation minimization for heat and mass transfer in a solid-gas reactor based on triangular element. J Phys D-Appl Phys, 2007, 40: 3545–3550

    Article  Google Scholar 

  49. Hajmohammadi M R, Rezaei E. Proposing a new algorithm for the optimization of conduction pathways based on a recursive localization. Appl Thermal Eng, 2019, 151: 146–153

    Article  Google Scholar 

  50. Hajmohammadi M R, Ahmadian M, Nourazar S S. Introducing highly conductive materials into a fin for heat transfer enhancement. Int J Mech Sci, 2019, 150: 420–426

    Article  Google Scholar 

  51. Naghibzadeh S K, Hajmohammadi M R, Saffar-Avval M. Heat transfer enhancement of a nanofluid in a helical coil with flattened cross-section. Chem Eng Res Des, 2019, 146: 36–47

    Article  Google Scholar 

  52. Chen L, Wei S, Sun F. Constructal entransy dissipation minimization for “volume-point” heat conduction. J Phys D-Appl Phys, 2008, 41: 195506

    Article  Google Scholar 

  53. Xiao Q H, Chen L G, Sun F R. Constructal entransy dissipation rate minimization for umbrella-shaped assembly of cylindrical fins. Sci China Tech Sci, 2011, 54: 211–219

    Article  MATH  Google Scholar 

  54. Xiao Q H, Chen L G, Xie Z H, et al. Constructal entransy dissipation rate minimization for Y-shaped assembly of fins (in Chinese). J Eng Thermophys, 2012, 33: 1465–1470

    Google Scholar 

  55. Xie Z H, Chen L G, Sun F R. Comparative study on constructal optimizations of T-shaped fin based on entransy dissipation rate minimization and maximum thermal resistance minimization. Sci China Tech Sci, 2011, 54: 1249–1258

    Article  MATH  Google Scholar 

  56. Feng H J, Chen L G, Sun F R. Constructal entransy dissipation rate minimization for leaf-like fins. Sci China Tech Sci, 2012, 55: 515–526

    Article  Google Scholar 

  57. Chen L, Xiao Q, Xie Z, et al. Constructal entransy dissipation rate minimization for tree-shaped assembly of fins. Int J Heat Mass Transfer, 2013, 67: 506–513

    Article  Google Scholar 

  58. Feng H J, Chen L G, Xie Z H, et al. Constructal optimization of complex fin with convective heat transfer based on entransy dissipation rate minimization (in Chinese). Acta Phys Sin, 2015, 64: 034701

    Google Scholar 

  59. Yang A B, Chen L G, Xie Z H, et al. Comparative study on constructal optimizations of rectangular fins heat sink based on entransy dissipation rate minimization and maximum thermal resistance minimization (in Chinese). Acta Phys Sin, 2015, 64: 204401

    Google Scholar 

  60. Harahap F, McManus Jr. H N. Natural convection heat transfer from horizontal rectangular fin arrays. J Heat Transfer, 1967, 89: 32–38

    Article  Google Scholar 

  61. Lorenzini G, Oliveira Rocha L A. Constructal design of Y-shaped assembly of fins. Int J Heat Mass Transfer, 2006, 49: 4552–4557

    Article  MATH  Google Scholar 

  62. Yang A B, Chen L G, Xie Z H, et al. Thermal performance analysis of non-uniform height rectangular fin based on constructal theory and entransy theory. Sci China Tech Sci, 2016, 59: 1882–1891

    Article  Google Scholar 

  63. Khan W A. Modeling of fluid flow and heat transfer for optimization of pin-fin heat sinks. Dissertation for Dcotoral Degree. Waterloo: University of Waterloo, 2004

    Google Scholar 

  64. Huang C H, Chen Y H. An optimal design problem in determining non-uniform fin heights and widths for an impingement heat sink module. Appl Thermal Eng, 2014, 63: 481–494

    Article  Google Scholar 

  65. Manjunath K, Kaushik S C. Entropy generation and thermo-economic analysis of constructal heat exchanger. Heat Trans Asian Res, 2014, 43: 39–60

    Article  Google Scholar 

  66. Bejan A, Badescu V, De Vos A. Constructal theory of economics. Appl Energy, 2000, 67: 37–60

    Article  Google Scholar 

  67. Zhou S, Chen L, Sun F. Optimization of constructal economics for volume-to-point transport. Appl Energy, 2007, 84: 505–511

    Article  Google Scholar 

  68. Azad AV, Amidpour M. Economic optimization of shell and tube heat exchanger based on constructal theory. Energy, 2011, 36: 1087–1096

    Article  Google Scholar 

  69. Yang A, Chen L, Xie Z, et al. Constructal operation cost minimization for in-line cylindrical pin-fin heat sinks. Int J Heat Mass Transfer, 2018, 129: 562–568

    Article  Google Scholar 

  70. Yu X L, Feng Q K, Feng J M. Research on the heat transfer and flow performance of a composite heat sink (in Chinese). J Xi’an Jiaotong Univ, 2003, 37: 670–673

    Google Scholar 

  71. Yu X L, Feng Q K, Feng J M. Research on thermal performance of plate-pin fin heat sink (in Chinese). J Xi’an Jiaotong Univ, 2004, 38: 1114–1118

    Google Scholar 

  72. Yuan W, Zhao J, Tso C P, et al. Numerical simulation of the thermal hydraulic performance of a plate pin fin heat sink. Appl Thermal Eng, 2012, 48: 81–88

    Article  Google Scholar 

  73. Zhao H, Liu Z, Zhang C, et al. Pressure drop and friction factor of a rectangular channel with staggered mini pin fins of different shapes. Exp Thermal Fluid Sci, 2016, 71: 57–69

    Article  Google Scholar 

  74. Muzychka Y S. Constructal design of forced convection cooled microchannel heat sinks and heat exchangers. Int J Heat Mass Transfer, 2005, 48: 3119–3127

    Article  MATH  Google Scholar 

  75. Bello-Ochende T, Liebenberg L, Meyer J P. Constructal design: Geometric optimization of micro-channel heat sinks. South African J Sci, 2007, 103: 483–489

    MATH  Google Scholar 

  76. Salimpour M R, Sharifhasan M, Shirani E. Constructal optimization of microchannel heat sinks with noncircular cross sections. Heat Transfer Eng, 2013, 34: 863–874

    Article  Google Scholar 

  77. Bello-Ochende T, Meyer J P, Ighalo F U. Combined numerical optimization and constructal theory for the design of microchannel heat sinks. Numer Heat Transfer Part A-Appl, 2010, 58: 882–899

    Article  Google Scholar 

  78. Adewumi O O, Bello-Ochende T, Meyer J P. Constructal design of single microchannel heat sink with varying axial length and temperature-dependent fluid properties. Int J Heat Tech, 2016, 34: S167–S172

    Article  Google Scholar 

  79. Mardani M, Salimpour M R. Optimization of triangular microchannel heat sinks using constructal theory. J Mech Sci Technol, 2016, 30: 4757–4764

    Article  Google Scholar 

  80. Khodabandeh E, Abbassi A. Performance optimization ofwater-Al2O3 nanofluid flow and heat transfer in trapezoidal cooling microchannel using constructal theory and two phase Eulerian-Lagrangian approach. Powder Tech, 2018, 323: 103–114

    Article  Google Scholar 

  81. Hajmohammadi M R, Alipour P, Parsa H. Microfluidic effects on the heat transfer enhancement and optimal design of microchannels heat sinks. Int J Heat Mass Transfer, 2018, 126: 808–815

    Article  Google Scholar 

  82. Wang Z H, Wang X D, Yan W M, et al. Multi-parameters optimization for microchannel heat sink using inverse problem method. Int J Heat Mass Transfer, 2011, 54: 2811–2819

    Article  MATH  Google Scholar 

  83. Vafai K, Zhu L. Analysis of two-layered micro-channel heat sink concept in electronic cooling. Int J Heat Mass Transfer, 1999, 42: 2287–2297

    Article  Google Scholar 

  84. Adewumi O O, Bello-Ochende T, Meyer J P. Geometric optimisation of multi-layered microchannel heat sink with different flow arrangements. In: Proceedings of the 15th International Heat Transfer Conference (IHTC-15). Kyoto, 2014. IHTC-9148

  85. Bello-Ochende T, Adewumi O O, Meyer J P. Increased heat load effects on the thermal performance of single- and two-layered microchannels with varying axial length and micro pin-fin inserts. Inter J Fluid Mech Res, 2016, 43: 441–455

    Article  Google Scholar 

  86. Adewumi O O, Bello-Ochende T, Meyer J P. Analysis of the thermal performance of single- and multi-layered microchannels with fixed volume constraint. Proc Roman Acad Ser A-Math Phys Tech Sci Inform Sci, 2018, 18: 154–159

    Google Scholar 

  87. Hajmohammadi M R, Toghraei I. Optimal design and thermal performance improvement ofa double-layered microchannel heat sink by introducing Al2O3 nano-particles into the water. Physica A-Statistical Mech its Appl, 2018, 505: 328–344

    Article  Google Scholar 

  88. Sarlak A, Ahmadpour A, Hajmohammadi M R. Thermal design improvement of a double-layered microchannel heat sink by using multi-walled carbon nanotube (MWCNT) nanofluids with non-Newtonian viscosity. Appl Thermal Eng, 2019, 147: 205–215

    Article  Google Scholar 

  89. Yang A B, Chen L G, Xie Z H, et al. Multi-objective optimization design for cylindrical pin-fin heat sinks based on the constructal theory (in Chinese). In: Proceedings of the 22nd National Academic Conference of Engineering Thermophysics in Colleges and Universities. Harbin, 2016

  90. Chen L, Yang A, Xie Z, et al. Constructal entropy generation rate minimization for cylindrical pin-fin heat sinks. Int J Thermal Sci, 2017, 111: 168–174

    Article  Google Scholar 

  91. Yang A, Chen L, Xie Z, et al. Constructal heat transfer rate maximization for cylindrical pin-fin heat sinks. Appl Thermal Eng, 2016, 108: 427–435

    Article  Google Scholar 

  92. Liu M Y, Xu X H, Laing X G. Numerical simulation and optimization on convective heat transfer characteristic in rectangular micro channel by high heat flux (in Chinese). J Eng Thermophys, 2010, 31: 633–636

    Google Scholar 

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Authors and Affiliations

  1. Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan, 430205, China

    LinGen Chen, HuiJun Feng, YanLin Ge & ShaoJun Xia

  2. School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan, 430205, China

    LinGen Chen, HuiJun Feng, YanLin Ge & ShaoJun Xia

  3. The 91404th Unit of PLA, Qinhuangdao, 066001, China

    AiBo Yang

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  1. LinGen Chen
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  2. AiBo Yang
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Correspondence to LinGen Chen.

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 51779262, 51506220 and 51579244).

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Chen, L., Yang, A., Feng, H. et al. Constructal design progress for eight types of heat sinks. Sci. China Technol. Sci. 63, 879–911 (2020). https://doi.org/10.1007/s11431-019-1469-1

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