Skip to main content
SpringerLink
Log in

Equivalent thermal resistance minimization for a circular disc heat sink with reverting microchannels based on constructal theory and entransy theory

  • Article
  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

Thermal designs for microchannel heat sinks with laminar flow are conducted numerically by combining constructal theory and entransy theory. Three types of 3-D circular disc heat sink models, i.e. without collection microchannels, with center collection microchannels, and with edge collection microchannels, are established respectively. Compared with the entransy equivalent thermal resistances of circular disc heat sink without collection microchannels and circular disc heat sink with edge collection microchannels, that of circular disc heat sink with center collection microchannels is the minimum, so the overall heat transfer performance of circular disc heat sink with center collection microchannels has obvious advantages. Furthermore, the effects of microchannel branch number on maximum thermal resistance and entransy equivalent thermal resistance of circular disc heat sink with center collection microchannels are investigated under different mass flow rates and heat fluxes. With the mass flow rate increasing, both the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number all gradually decrease. With the heat flux increasing, the maximum thermal resistances and the entransy equivalent thermal resistances of heat sinks with respective fixed microchannel branch number remain almost unchanged. With the same mass flow rate and heat flux, the larger the microchannel branch number, the smaller the maximum thermal resistance. While the optimal microchannel branch number corresponding to minimum entransy equivalent thermal resistance is 6.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sohel Murshed S M, Nieto de Castro C A. A critical review of traditional and emerging techniques and fluids for electronics cooling. Renew Sustain Energy Rev, 2017, 78: 821–833

    Google Scholar 

  2. 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

    MathSciNet  MATH  Google Scholar 

  3. 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

    Google Scholar 

  4. He Y L, Tao W Q. Convective heat transfer enhancement: Mechanisms, techniques, and performance evaluation. Adv Heat Transfer, 2014, 46: 87–186

    Google Scholar 

  5. Wei L, Zhichun L, Tingzhen M, et al. Physical quantity synergy in laminar flow field and its application in heat transfer enhancement. Int J Heat Mass Transfer, 2009, 52: 4669–4672

    MATH  Google Scholar 

  6. Luo X, Hu R, Liu S, et al. Heat and fluid flow in high-power LED packaging and applications. Prog Energy Combust Sci, 2016, 56: 1–32

    Google Scholar 

  7. Xie G, Li Y, Zhang F, et al. Analysis of micro-channel heat sinks with rectangular-shaped flow obstructions. Numer Heat Transfer Part A-Appl, 2016, 69: 335–351

    Google Scholar 

  8. Hu D H, Zhang Z W, Li Q. Numerical study on flow and heat transfer characteristics of microchannel designed using topological optimizations method. Sci China Technol Sci, 2020, 63: 105–115

    Google Scholar 

  9. Bejan A. Street network theory of organization in nature. J Adv Transport, 1996, 30: 85–107

    Google Scholar 

  10. Reis A H. Constructal theory: From engineering to physics, and how flow systems develop shape and structure. Appl Mech Rev, 2006, 59: 269–282

    Google Scholar 

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

    Google Scholar 

  12. Bejan A. Constructal thermodynamics. Int J Heat Tech, 2016, 34: S1–S8

    Google Scholar 

  13. Bejan A, Errera M R. Complexity, organization, evolution, and constructal law. J Appl Phys, 2016, 119: 074901

    Google Scholar 

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

    Google Scholar 

  15. 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

    Google Scholar 

  16. Lorente S. The constructal law: From microscale to urban-scale design. Ann Rev Heat Transfer, 2017, 19: 335–368

    Google Scholar 

  17. Chen L G, Xiao Q H, Feng H J. 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

    Google Scholar 

  18. Lorente S. Constructal law: From microscale to urban-scale design. Ann Rev Heat Transfer, 2016, 19: 335–368

    Google Scholar 

  19. Bejan A, Gunes U, Sahin B. The evolution of air and maritime transport. Appl Phys Rev, 2019, 6: 021319

    Google Scholar 

  20. 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

    Google Scholar 

  21. Lorente S, Bejan A. Current trends in constructal law and evolutionary design. Heat Trans Asian Res, 2019, 48: 3574–3589

    Google Scholar 

  22. Bejan A, Lorente S. Design with Constructal Theory. New Jersey: Wiley, 2008

    MATH  Google Scholar 

  23. Rocha L A O, Lorente S, Bejan A. Constructal Law and the Unifying Principle of Design. Berlin: Springer, 2013

    Google Scholar 

  24. 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 

  25. Bejan A. Freedom and Evolution: Hierarchy in Nature, Society and Science. Springer, 2020

  26. Chen L G, Yang A B, Feng H J, et al. Constructal designs progress for eight types of heat sinks. Sci China Tech Sci, 2020, 63: 879–911

    Google Scholar 

  27. Feng H, Chen L, Xia S. Constructal design for disc-shaped heat exchanger with maximum thermal efficiency. Int J Heat Mass Transfer, 2019, 130: 740–746

    Google Scholar 

  28. Feng H, Chen L, Wu Z, et al. Constructal design of a shell-and-tube heat exchanger for organic fluid evaporation process. Int J Heat Mass Transfer, 2019, 131: 750–756

    Google Scholar 

  29. Chen L, You J, Feng H, et al. Constructal optimization for “disc-point” heat conduction with nonuniform heat generating. Int J Heat Mass Transfer, 2019, 134: 1191–1198

    Google Scholar 

  30. You J, Feng H, Chen L, et al. Constructal design of nonuniform heat generating area based on triangular elements: A case of entropy generation minimization. Int J Thermal Sci, 2019, 139: 403–412

    Google Scholar 

  31. You J, Feng H, Chen L, et al. Constructal design and experimental validation of a non-uniform heat generating body with rectangular cross-section and parallel circular cooling channels. Int J Heat Mass Transfer, 2020, 148: 119028

    Google Scholar 

  32. Feng H, You J, Chen L, et al. Constructal design of a non-uniform heat generating disc based on entropy generation minimization. Eur Phys J Plus, 2020, 135: 257

    Google Scholar 

  33. Cai C, Feng H, Chen L, et al. Constructal design of a shell-and-tube evaporator with ammonia-water working fluid. Int J Heat Mass Transfer, 2019, 135: 541–547

    Google Scholar 

  34. Xie Z, Feng H, Chen L, et al. Constructal design for supercharged boiler evaporator. Int J Heat Mass Transfer, 2019, 138: 571–579

    Google Scholar 

  35. Wu Z, Feng H, Chen L, et al. Pumping power minimization of an evaporator in ocean thermal energy conversion system based on constructal theory. Energy, 2019, 181: 974–984

    Google Scholar 

  36. Feng H, Xie Z, Chen L, et al. Constructal design for supercharged boiler superheater. Energy, 2020, 191: 116484

    Google Scholar 

  37. Wu Z, Feng H, Chen L, et al. Optimal design of dual-pressure turbine in OTEC system based on constructal theory. Energy Convers Manage, 2019, 201: 112179

    Google Scholar 

  38. Wu Z, Feng H, Chen L, et al. Constructal thermodynamic optimization for ocean thermal energy conversion system with dual-pressure organic Rankine cycle. Energy Convers Manage, 2020, 210: 112727

    Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  41. Chen L, Feng H, Xie Z, et al. Thermal efficiency maximization for H- and X-shaped heat exchangers based on constructal theory. Appl Thermal Eng, 2015, 91: 456–462

    Google Scholar 

  42. Xie Z H, Chen L G, Sun F R. Constructal optimization of H-shaped vasculature with convective heat transfer based on minimization of entropy generation rate (in Chinese). J Therm Sci Tech, 2011, 10: 269–277

    Google Scholar 

  43. Xie Z, Chen L, Sun F. Constructal entropy generation rate minimization of line-to-line vascular networks with convective heat transfer. Int J Thermal Sci, 2013, 74: 72–80

    Google Scholar 

  44. Fan X, Xie Z, Sun F, et al. Convective heat transfer characteristics of line-to-line vascular microchannel heat sink with temperature-dependent fluid properties. Appl Thermal Eng, 2016, 93: 606–613

    Google Scholar 

  45. Ghaedamini H, Salimpour M R, Campo A. Constructal design of reverting microchannels for convective cooling of a circular disc. Int J Thermal Sci, 2011, 50: 1051–1061

    Google Scholar 

  46. Farzaneh M, Salimpour M R, Tavakoli M R. Design of bifurcating microchannels with/without loops for cooling of square-shaped electronic components. Appl Thermal Eng, 2016, 108: 581–595

    Google Scholar 

  47. Farzaneh M, Tavakoli M R, Salimpour M R. Effect of reverting channels on heat transfer performance of microchannels with different geometries. J Appl Fluid Mech, 2017, 10: 41–53

    Google Scholar 

  48. 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

    MATH  Google Scholar 

  49. Chen Q, Wang M, Pan N, et al. Optimization principles for convective heat transfer. Energy, 2009, 34: 1199–1206

    Google Scholar 

  50. Hu G J, Cao B Y, Guo Z Y. Entransy and entropy revisited. Chin Sci Bull, 2011, 56: 2974–2977

    Google Scholar 

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

    Google Scholar 

  52. 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

    Google Scholar 

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

    Google Scholar 

  54. Zhang T, Liu X H, Tang H D, et al. Progress of entransy analysis on the air-conditioning system in buildings. Sci China Technol Sci, 2016, 59: 1463–1474

    Google Scholar 

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

    Google Scholar 

  56. Chen X, Zhao T, Zhang M Q, et al. Entropy and entransy in convective heat transfer optimization: A review and perspective. Int J Heat Mass Transfer, 2019, 137: 1191–1220

    Google Scholar 

  57. Liang X G, Chen Q, Guo Z Y. Entransy Theory for Heat Transfer Analyses and Optimizations (in Chinese). Beijing: Science Press, 2019

    Google Scholar 

  58. Chen Q, Ren J X. Generalized thermal resistance for convective heat transfer and its relation to entransy dissipation. Chin Sci Bull, 2008, 53: 3753–3761

    Google Scholar 

  59. Zhao T, Chen Q. Macroscopic physical meaning of entransy and its application (in Chinese). Acta Phys Sin, 2013, 62: 234401

    Google Scholar 

  60. 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

    Google Scholar 

  61. Liu W, Liu Z C, Jia H, et al. Entransy expression of the second law of thermodynamics and its application to optimization in heat transfer process. Int J Heat Mass Transfer, 2011, 54: 3049–3059

    MATH  Google Scholar 

  62. Huang Z W, Li Z N, Hwang Y, et al. Application of entransy dissipation based thermal resistance to design optimization of a novel finless evaporator. Sci China Technol Sci, 2016, 59: 1486–1493

    Google Scholar 

  63. Li T L, Yuan Z H, Xu P, et al. Entransy dissipation/loss-based optimization of two-stage organic Rankine cycle (TSORC) with R245fa for geothermal power generation. Sci China Technol Sci, 2016, 59: 1524–1536

    Google Scholar 

  64. Cheng X T, Zhao J M, Liang X G. Discussion on the extensions of the entransy theory. Sci China Technol Sci, 2017, 60: 363–373

    Google Scholar 

  65. Wu Y Q. Analyses of thermodynamic performance for the endoreversible Otto cycle with the concepts of entropy generation and entransy. Sci China Technol Sci, 2017, 60: 692–700

    Google Scholar 

  66. Cheng X T, Liang X G. Entransy analyses of the thermodynamic cycle in a turbojet engine. Sci China Technol Sci, 2017, 60: 1160–1167

    Google Scholar 

  67. Hua Y C, Zhao T, Guo Z Y. Optimization of the one-dimensional transient heat conduction problems using extended entransy analyses. Int J Heat Mass Transfer, 2018, 116: 166–172

    Google Scholar 

  68. Goudarzi N, Talebi S. Heat removal ability for different orientations of single-phase natural circulation loops using the entransy method. Ann Nucl Energy, 2018, 111: 509–522

    Google Scholar 

  69. Cheng X T, Xu X H, Liang X G. Theoretical analyses of the performance of a concentrating photovoltaic/thermal solar system with a mathematical and physical model, entropy generation minimization and entransy theory. Sci China Technol Sci, 2018, 61: 843–852

    Google Scholar 

  70. Geete A. Aanlyses of entransy dissipation ratio and entropy generation ratio for fas power cycles under various conditions: Edeg software. Heat Trans Res, 2019, 50: 1–16

    Google Scholar 

  71. Naik B K, Muthukumar P. Energy, entransy and exergy analyses of a liquid desiccant regenerator. Int J Refrigeration, 2019, 105: 80–91

    Google Scholar 

  72. Zhao T, Liu D, Chen Q. A collaborative optimization method for heat transfer systems based on the heat current method and entransy dissipation extremum principle. Appl Thermal Eng, 2019, 146: 635–647

    Google Scholar 

  73. Cheng X T, Liang X G. Entransy functions for steady heat transfer. Sci China Technol Sci, 2019, 62: 1726–1734

    Google Scholar 

  74. Gülten A. Determination of optimum insulation thickness using the entransy based thermoeconomic and environmental analysis: a case study for Turkey. Energy Sources Part A-Recovery Utilization Environ Effects, 2020, 42: 219–232

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  77. Xie Z H, Chen L G, Sun F R. Constructal optimization for geometry of cavity by taking entransy dissipation minimization as objective. Sci China Ser E-Technol Sci, 2009, 52: 3504–3513

    MATH  Google Scholar 

  78. 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 Technol Sci, 2011, 54: 1249–1258

    MATH  Google Scholar 

  79. 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 Technol Sci, 2016, 59: 1882–1891

    Google Scholar 

  80. Chen L G, Wang L, Xie Z H, et al. Constructal studies on hexagonal microchannel heat sinks based on multi-physics field coupling calculations (in Chinese). Sci Sin Tech, 2019, 49: 741–752

    Google Scholar 

  81. Feng H J, Sun F R, Xie Z H, et al. Constructal optimization for “discpoint” vascular networks based on minimum entransy dissipation rate (in Chinese). Sci Sin Tech, 2014, 44: 71–80

    Google Scholar 

  82. Feng H J, Chen L G, Xie Z H. Constructal entransy dissipation rate minimization for X-shaped vascular networks. Sci China Technol Sci, 2019, 62: 2195–2203

    Google Scholar 

  83. Feng H J, Chen L G, Wu Z X, et al. Constructal optimization for an organic fluid shell-and-tube heat exchanger based on entransy theory (in Chinese). Sci Sin Tech, 2020, doi: https://doi.org/10.1360/SST-2019-0246

  84. COMSOL Multiphysics User’s Guide. Version 5.2a. Sweden: COMSOL Incorporated, 2012, 103–147

  85. Wang X Q, Yap C, Mujumdar A S. Laminar heat transfer in constructal microchannel networks with loops. J Electron Packaging, 2006, 128: 273–280

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Power Engineering, Naval University of Engineering, Wuhan, 430033, China

    Liang Wang, ZhiHui Xie & Rong Wang

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

    ZhiHui Xie, LinGen Chen & HuiJun Feng

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

    ZhiHui Xie, LinGen Chen & HuiJun Feng

Authors
  1. Liang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. ZhiHui Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. LinGen Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. HuiJun Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to ZhiHui Xie or LinGen Chen.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51979278, 51579244 and 51506220). The authors wish to thank the reviewers for their careful, unbiased and constructive suggestions, which led to this revised manuscript.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, L., Xie, Z., Chen, L. et al. Equivalent thermal resistance minimization for a circular disc heat sink with reverting microchannels based on constructal theory and entransy theory. Sci. China Technol. Sci. 64, 111–121 (2021). https://doi.org/10.1007/s11431-020-1578-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-020-1578-6

Keywords

Search

Navigation