Skip to main content
SpringerLink
Log in

Constructal Solid and Perforated Fin Installation in a Combined Microchannel Heat Sink for Maximum Heat Transfer

  • Original Contribution
  • Published:
Journal of The Institution of Engineers (India): Series C Aims and scope Submit manuscript

Abstract

This paper details the numerical analysis of combined microchannels with solid and perforated rectangular fins. The goal of the numerical process is to maximise global thermal conductance in the geometric configurations studied. Three scenarios are investigated: a microchannel with solid rectangular fins, a microheat sink with single square perforation on the fins and a combined microchannel with two square perforations. The volume and axial length of the combined microchannel are fixed, while the width varies. An imposed high-density heat flux \({q}^{{\prime\prime}}\) of 250 W/cm2 is applied at the bottom surface of the combined microchannels with fins. Water is used as a coolant to remove the heat deposited at the channel walls and the entire microchannel heat sink. The finite volume method in Ansys Fluent is employed to discretise the computational domain and the thermal and fluid fields solved. The results showed that hydraulic diameter, external aspect ratio and Reynolds number of water \(({\mathrm{Re}}_{{w}})\) have an effect on minimised temperature and global thermal conductance. When the Reynolds number of fluid increases by 20%, the minimised temperature diminishes by 2.6, 2.5 and 2.1%, in the three configurations investigated. The numerical optimisation shows that the combined microchannel with two square perforations on fins is the best. The design technique and innovation employed to reduce the volume, weight, cost of production and solid substrate used in the heat sink manufacturing enhanced the performance and increased heat transfer. The numerical code validation is carried out using analytical results.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

A :

Cross-sectional area of a channel

C :

Dimensionless thermal conductance

d :

Diameter

d h :

Hydraulic diameter

H :

Height of heat sink

k f :

Fluid thermal conductivity

k s :

Solid wall thermal conductivity

MCH:

Microchannel

N :

Heat sink axial length

n :

Number of channels

\({q}^{{\prime\prime}}\) :

Heat flux

Rew :

Reynolds number of water

T w,L :

Exit temperature

T in :

Inlet temperature

T max :

Maximum temperature

t 1 :

Channel distance from bottom

t 2 :

Channel distance from the top microheat sink

t 3 :

Thickness from channel to channel

v in :

Inlet velocity

V :

Volume

v el :

Elemental volume

W :

Width of a microchannel heat sink

α :

Thermal diffusivity

C p :

Specific heat

µ :

Viscosity

ν :

Kinematic viscosity

ρ :

Density

ϕ :

Porosity

τ :

Shear stress

in:

Inlet

max:

Maximum

min:

Minimum

opt:

Optimum

out:

Outlet

References

  1. ANSYS 18.1 Design Xplorer, User’s Guide. (2017). www.fluent.com.

  2. A.I. Khuri, S. Mukhopadhyay, Response surface methodology. Wiley Interdiscip. Rev. Comput. Stat. 2(2), 128–149 (2010). https://doi.org/10.1002/wics.73

    Article  Google Scholar 

  3. G.E.P. Box, K.B. Wilson, On the experimental attainment of optimum conditions. J. R. Stat. Soc. B 13(1), 1–45 (1951). https://doi.org/10.1111/j.2517-6161.1951.tb00067.x

    Article  MathSciNet  Google Scholar 

  4. S.J. Kahil, F. Maugeri, M.I. Rodrigues, Response surface analysis and simulation as a tool for bioprocess design and optimization. Process Biochem. 35(6), 539–550 (2000). https://doi.org/10.1016/S0032-9592(99)00101-6

    Article  Google Scholar 

  5. J.S. Shang, S. Li, P. Tadikamalla, Operational design of a supply chain system using the Taguchi method, response surface methodology, simulation, and optimization. Int. J. Prod. Res. 42(18), 3823–3825 (2004). https://doi.org/10.1080/00207540410001704050

    Article  Google Scholar 

  6. R.R. Barton, Metamodels for simulation input–output relations, in Proc. Winter Simul Conf., Arlington, VA, (1992), pp. 289–299. https://doi.org/10.1145/167293.167352

  7. R.R. Barton, Simulation metamodels, in Proceeding Winter Simul Conf., Washington, DC (1998), pp. 167–174. https://doi.org/10.1109/WSC.1998.744912

  8. J.H. Noguera, E.F. Watson, Response surface analysis of a multi-product batch processing facility using a simulation metamodel. Int. J. Econ. Prod. 102(2), 333–343 (2006). https://doi.org/10.1504/EJIE.2014.059351

    Article  Google Scholar 

  9. T.W. Simpson, J.D. Peplinski, P.N. Koch, J.K. Allen, Metamodels for computer-based engineering design: survey and recommendations, in ASME Des. Eng. Tech. Conf., Sacramento, California USA (1997), pp. 1–14. https://doi.org/10.1007/PL00007198

  10. R.R. Barton, Simulation experiment design, in Proceedings of the 2010 Winter Simulation Conference, ed. by B. Johansson, S. Jain, J. Montoya-Tones, J. Hugan, E. Yucesan (2010), pp. 75–86. https://doi.org/10.1109/WSC.2010.5679171

  11. D.Q. Kern, A.D. Kraus, Extended Surface Heat Transfer (McGraw-Hill book, New York, 1972). https://doi.org/10.4236/epe.2011.32022

  12. Y. Han, Y. Liua, M. Liaa, J. Huanga, A review of development of micro-channel heat exchanger applied in air-conditioning system. Energy Procedia 14(2012), 148–153 (2012)

    Article  Google Scholar 

  13. T.S. Ravigururajan, J. Cuta, C.E. McDonald, M.K. Drost, Effects of heat flux on two-phase flow characteristics of refrigerant flows in a micro-channel heat exchanger. National heat transfer conference, American Society of Mechanical Engineers, Houston, TX (United States), USA, 3–6 Aug 1996 (1996), p. 261.

  14. J. Li, G.P. Peterson, 3-Dimensional numerical optimization of silicon-based high performance parallel microchannel heat sink with liquid flow. Int. J. Heat Mass Transf. 50(15–16), 2895–2904 (2007). https://doi.org/10.1109/TCAPT.2005.853170

    Article  Google Scholar 

  15. W. Qu, I. Mudawar, Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink. Int. J. Heat Mass Transf. 45(12), 2549–2565 (2001). https://doi.org/10.1016/S0017-9310(01)00337-4

    Article  Google Scholar 

  16. T. Bello-Ochende, O.T. Olakoyejo, J.P. Meyer, A. Benjan, S. Lorente, Constructal flow orientation in conjugate cooling channels with internal heat generation. Int. J. Heat Mass Transf. 57(1), 241–249 (2013). https://doi.org/10.1016/j.ijheatmasstransfer.2012.10.021

    Article  Google Scholar 

  17. K.K. Ambatipudi, M.M. Rahman, Analysis of conjugate heat transfer in microchannel heat sinks. Numer. Heat Transf. Part A Appl. 37(7), 711–731 (2000). https://doi.org/10.1080/104077800274046

    Article  ADS  Google Scholar 

  18. A.K. Pramanick, The Nature of Motive Force (Springer, New York, 2014)

    Book  Google Scholar 

  19. A.K. Pramanick, Philosophy of Nature, Reflection Magazine, (R. E. College Durgapur, 1991), pp. 2–5.

  20. S. Carnot, Reflections on the Motive Power of Fire (trans: R. H. Thurston) (Dover, New York, 2005).

  21. M.J. Klein, Carnot’s contribution to thermodynamics. Phys. Today 27, 23–28 (1974). https://doi.org/10.1063/1.3128802

    Article  CAS  Google Scholar 

  22. A.K. Pramanick, An asymptotic approach to law of motive force and constructal law. Rev. Roum. Sci. Techn. – Électrotechn. et Énerg. 64(3), 293–296 (2019). https://doi.org/10.1115/1.2204075

  23. A.K. Pramanick, Heat and Mass Transfer: The Law of Motive Force (Springer, Heidelberg, 2014)

    Google Scholar 

  24. A. Bejan, Advanced Engineering Thermodynamics (Wiley, New York, 1997), p.807

    Google Scholar 

  25. O.T. Olakoyejo, T. Bello-Ochende, J.P. Meyer, Constructal conjugate cooling channels with internal heat generation. Int. J. Heat Mass Transf. 55(15), 4385–4396 (2012). https://doi.org/10.1016/j.ijheatmasstransfer.2012.04.007

    Article  Google Scholar 

  26. A. Bejan, S. Lorente, The constructal law and the evolution of design in nature. Phys. Life Rev. 8(3), 209–240 (2011). https://doi.org/10.1016/j.plrev.2011.05.010

    Article  PubMed  ADS  Google Scholar 

  27. O.T. Olakoyejo, T. Bello-Ochende, J.P. Meyer, Mathematical optimization of laminar forced convection heat transfer through a vascularised solid with square channels. Int. J. Heat Mass Transf. 55(9), 2402–2411 (2012). https://doi.org/10.1016/j.ijheatmasstransfer.2011.12.036

    Article  Google Scholar 

  28. M.R. Salimpour, M. Sharifhasan, E. Shirani, Constructal optimization of the geometry of an array of micro-channels. Int. Heat Mass Transf. 38(1), 93–99 (2011). https://doi.org/10.1080/01457632.2012.746552

    Article  CAS  Google Scholar 

  29. M.R. Salimpour, M. Sharifhasan, E. Shirani, Constructal optimization of microchannel heat sinks with noncircular cross sections. Heat Transf. Eng. 34(10), 863–874 (2013). https://doi.org/10.1080/01457632.2012.746552

    Article  CAS  ADS  Google Scholar 

  30. J.H. Ryu, D.H. Choi, S.J. Kim, Three-dimensional numerical optimization of a manifold micro channel heat sink. PERGAMON 46(9), 1553–1562 (2003). https://doi.org/10.1016/S0017-9310(02)00443-X

    Article  Google Scholar 

  31. A. Bejan, Heat Transfer (John Willey & Son, New Jersey, 1993)

    Google Scholar 

  32. B. Prabhakar, P.K. Yogesh, Thermal performance of open microchannel heat sink with variable pin fin height. Int. J. Therm. Sci. 159, 1066 (2021)

    Google Scholar 

  33. Y.K. Prajapati, Influence of fin height on heat transfer and fluid flow characteristics of rectangular microchannel heat sink. Int. J. Heat Mass Transf. 137, 1041–1052 (2019)

    Article  CAS  Google Scholar 

  34. M. Tahat, Z.H. Kodah, B.A. Jarrah, S.D. Probert, Heat transfers from pin-fin arrays experiencing forced convection. Appl. Energy 67(4), 419–422 (2000)

    Article  ADS  Google Scholar 

  35. A. Kosar, C. Mishra, Y. Peles, Laminar flow across a bank of low aspect ratio micro pin fins. J. Fluids Eng. 127(3), 419 (2005)

    Article  Google Scholar 

  36. A. Kosar, Y. Peles, Thermal- hydraulic performance of MEMS-based pin fin heat sink. J. Heat Transfer 128(2), 121–131 (2006)

    Article  CAS  Google Scholar 

  37. A.M. Siu-Ho, W. Qu, F. Pfefferkom, Experimental study of pressure drop and heat transfer in a single-phase micropin-fin heat sink. J. Electron. Packag. 129(4), 479–487 (2007)

    Article  CAS  Google Scholar 

  38. N.Y. Godi, M.O. Petinrin, Heat transfer analysis in constructal designed microchannels with perforated micro fins. J. Inst. Eng. India Ser. C (2023). https://doi.org/10.1007/s40032-023-00943-y

    Article  Google Scholar 

  39. R.H. Yeh, An analytical study of the optimum dimension of rectangular fins and cylindrical pin fins. Int. J. Heat Mass Transf. 40, 3607–3615 (1997). https://doi.org/10.1016/s0017-9310(97)00010-0

    Article  CAS  Google Scholar 

  40. Y. Peles, A. Kosar, C. Mishra, K. Chih-Jung, S. Brandon, Forced convective heat transfer across a pin fin micro heat sink. Int. J. Heat Mass Transf. 48, 3615–3627 (2005). https://doi.org/10.1016/j.ijheatmasstransfer.2005.03.017

    Article  CAS  Google Scholar 

  41. V.S. Achanta, An experimental study of end wall heat transfer enhancement or flow staggered non-conducting pin fin arrays, PhD Thesis, Department of Mechanical Engineering, Texas A & M University, U.S.A (2003).

  42. M.E. Lyall. Heat transfer from low aspect ratio pin fin, PhD thesis, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University (2006).

  43. M. Vilarrubí, S. Riera, M. Ibañez, M. Omri, G. Lagun, L. Fréchette, J. Barra, Experimental and numerical study of micro-pin-fin heat sinks with variable density for increased temperature uniformity. Int. J. Therm. Sci. 132, 424–434 (2018). https://doi.org/10.1016/j.ijthermalsci.2018.06.019

    Article  Google Scholar 

  44. B. Sahin, A. Demir, Thermal performance analysis and optimum design parameters of heat exchanger having perforated pin fins. Energy Convers. Manag. 49, 1684–1695 (2008)

    Article  CAS  Google Scholar 

  45. M. Yaghoubi, E. Velayati, Undeveloped convective heat transfer from an array of cubes in cross-stream direction. Int. J. Therm. Sci. 44, 756–765 (2005). https://doi.org/10.1016/j.ijheatmasstransfer.2005.03.017

    Article  CAS  Google Scholar 

  46. M.R. Sheri, M. Yaghoubi, K. Jafarpur, Heat transfer analysis of lateral perforated fin heat sinks. Appl. Energy 86, 2019–2029 (2009). https://doi.org/10.1016/j.enconman.2009.01.021

    Article  CAS  ADS  Google Scholar 

  47. O.O. Adewumi, T. Bello-Ochende, J.P. Meyer, Constructal design of combined microchannel and micro pin fins for electronic cooling. Int. J. Heat Mass Transf. 66, 215–323 (2013). https://doi.org/10.1016/j.ijheatmasstransfer.2013.07.039

    Article  Google Scholar 

  48. F. Laermer, A. Urban, Challenges, development and applications of silicon deep reactive ion etching. Microelectron. Eng. 67–68, 349–355 (2003). https://doi.org/10.1016/S0167-9317(03)00089-3

    Article  CAS  Google Scholar 

  49. M.J. Madon, in: MEMS Handb, ed. by M. Gad-el-Hak (CRC Press, Taylor & Francis Group, 2002), p. 1368. https://doi.org/10.1201/9780429103872

  50. F.U. Ighalo, Optimisation of microchannels and micro pin-fin heat sinks with computational fluid dynamics in combination with a mathematical optimisation algorithm, MSc. Thesis Department of Mechanical and Aeronautical Engineering, University of Pretoria, (2010).

  51. C.L. Chen, C.H. Cheng, Numerical study of the effects of lid oscillation on the periodic flow pattern and convection heat transfer in a triangular cavity. Int. Commun. Heat Mass Transf. 36, 590–596 (2009). https://doi.org/10.1016/j.icheatmasstransfer.2009.03.006

    Article  Google Scholar 

  52. L. Chai, G.D. Xia, M.Z. Zhou et al., Numerical simulation of fluid flow and heat transfer in a microchannel heat sink with offset fan-shaped reentrant cavities in sidewall. Int. Commun. Heat Mass Transf. 38, 577–584 (2011). https://doi.org/10.1016/j.icheatmasstransfer.2010.12.037

    Article  Google Scholar 

  53. L.S. Ismail, C. Ranganayakulu, R.K. Shah, Numerical study of flow patterns of compact plate-fin heat exchangers and generation of design data for offset and wavy fins. Int. J. Heat Mass Transf. 52, 3972–3983 (2009). https://doi.org/10.1016/j.ijheatmasstransfer.2009.03.026

    Article  CAS  Google Scholar 

  54. S.V. Patankar, Numerical heat transfer and fluid flow. CRC Press (2018). https://doi.org/10.1201/9781482234213

    Article  Google Scholar 

  55. F.M. White, Viscous Fluid Flow (McGraw-Hill, Inc., New York, 1991)

    Google Scholar 

  56. J. Kepler, The Six-Cornered Snowflake (Clarendon Press, Oxford, 1966)

    Google Scholar 

  57. W.A. Khan, J.R. Culham, M.M. Yovanovich, Modelling of cylindrical pin-fin heat sinks for electronic packaging. IEEE Trans. Compon. Packag. Technol. 31(3), 536–545 (2008). https://doi.org/10.2514/1.17713

    Article  Google Scholar 

  58. O.O. Adewumi, Constructal design and optimisation of combined microchannel and micro pin fins for microelectronic cooling, University of Pretoria (2016).

Download references

Acknowledgements

The author appreciates the University of Cape Town, SA and Modibbo Adama University, Yola, for the facilities and support provided during the research.

Funding

The author has not disclosed any funding.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Cape Town, Private Bag X3, Rondebosch, 7701, South Africa

    N. Y. Godi

Authors
  1. N. Y. Godi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Y. Godi.

Ethics declarations

Conflict of interest

The author declares no conflicts of interest associated with this publication

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Godi, N.Y. Constructal Solid and Perforated Fin Installation in a Combined Microchannel Heat Sink for Maximum Heat Transfer. J. Inst. Eng. India Ser. C 105, 17–30 (2024). https://doi.org/10.1007/s40032-023-01006-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40032-023-01006-y

Keywords

Search

Navigation