Heat transfer performance of a porous copper micro-channel heat sink

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A novel porous copper micro-channel heat sink based on the high thermal conductivity and structural stability of porous copper micro-channel material is proposed in this study. A circular cross-sectional and a multi-layer staggered arrangement are the main characteristics of the micro-channel heat sink. Additionally, a heat dissipation model is produced for porous copper micro-channel heat sink by analyzing the heat transfer process. Further, the theoretical heat transfer coefficient is calculated using MATLAB, and the experimental heat transfer coefficient is determined based on an experimental platform. The heat dissipation model is verified by comparing the theoretical and experimental heat transfer coefficients. The relation between the porous copper micro-channel heat sink parameters and the heat transfer coefficient that is obtained based on the heat dissipation model of the porous copper micro-channel heat sink is analyzed. The results exhibit that variations in pore diameter, porosity, porous copper length, porous copper width, porous copper height, and volume flow significantly affect the heat transfer performance.

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A :

Contact area between the copper panel and the bottom surface of porous copper (m2)

c a :

Surface density coefficient of porous copper

c b :

Heat exchange efficiency

c H :

Bending coefficient of corrugated wall

c p :

Fluid heat capacity (J kg−1 K−1)

d :

Pore diameter (m)

G :

Mass flow rate (kg m−2 s−1)

H :

Porous copper height (m)

h :

Heat transfer coefficient of porous copper micro-channel heat sink (W m−2 K−1)

h 0 :

Heat transfer coefficient of corrugated wall and coolant in x axis section (W m−2 K−1)

I :

Current (A)

k :

Thermal conductivity (W m−1 K−1)

L :

Porous copper length (m)

Nu :

Nusselt number

P :

Fluid pressure (Pa)

Q :

Heat (W)

Q 1 :

Heat of ceramic heating plate (W)

Q 2 :

Absorbed heat of coolant (W)

q 0 :

Heat flux (W m−2)

S :

Distance between the surface of micro-channel and the location of thermocouple (m)

T :

Temperature (K)

T w :

Temperature of thermocouple point (K)

t :

Thickness of hole wall (m)

U :

Voltage (V)

V l :

Volume flow (m3 s−1)

v 0 :

Flow velocity (m s−1)

W :

Porous copper width (m)



ε :

Porosity (%)

ε Q :

Uncertainty of heat (%)

ρ f :

Fluid density (kg m−3)

μ f :

Fluid kinetic viscosity (kg m−1 s−1)

f :


s :







  1. 1.

    Sarafraz MM, Nikkhah V, Nakhjavani M, Arya A. Fouling formation and thermal performance of aqueous carbon nanotube nanofluid in a heat sink with rectangular parallel micro-channel. Appl Therm Eng. 2017;123:29–39.

  2. 2.

    Sarafraz MM, Nikkhah V, Nakhjavani M, Arya A. Thermal performance of a heat sink micro-channel working with biologically produced silver-water nanofluid: experimental assessment. Exp Therm Fluid Sci. 2018;91:509–19.

  3. 3.

    Tuckerman DB, Pease RFW. High-performance heat sinking for VLSI. IEEE Electron Device Lett. 1981;2(5):126–9.

  4. 4.

    Wei XJ, Joshi Y. Stacked micro-channel heat sinks for liquid cooling of microelectronic components. J Electron Packag. 2004;126(1):60–6.

  5. 5.

    Wei XJ, Joshi Y, Patterson MK. Experimental and numerical study of a stacked micro-channel heat sink for liquid cooling of microelectronic devices. J Heat Transf. 2007;129(10):1432–44.

  6. 6.

    Khodabandeh E, Tozati SA, Joshaghani M, Akbari OA. Thermal performance improvement in water nanofluid/GNP-SDBS in novel design of double-layer microchannel heat sink with sinusoidal cavities and rectangular ribs. J Therm Anal Calorim. 2019;136:1333–45.

  7. 7.

    Vafai K, Zhu L. Analysis of two-layered micro-channel heat sink concept in electronic cooling. Int J Heat Mass Transf. 1999;42(12):2287–97.

  8. 8.

    Hung TC, Yan WM, Li WP. Analysis of heat transfer characteristics of double-layered micro-channel heat sink. Int J Heat Mass Transf. 2012;55(11–12):3090–9.

  9. 9.

    Tang B, Zhou R, Bai PF, Fu T, Lu LS, Zhou GF. Heat transfer performance of a novel double-layer mini-channel heat sink. Heat Mass Transf. 2017;53:929–36.

  10. 10.

    Gu S, Lu TJ, Evans AG. On the design of two-dimensional cellular metals for combined heat dissipation and structural load capacity. Int J Heat Mass Transf. 2001;44:2163–75.

  11. 11.

    Eastman JA, Choi SUS, Li S, Yu W, Thompson LJ. Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl Phys Lett. 2001;78(6):718–20.

  12. 12.

    Topuz A, Engin T, Özalp AA, Erdogan B, Mert S, Yeter A. Experimental investigation of optimum thermal performance and pressure drop of water-based Al2O3, TiO2 and ZnO nanofluids flowing inside a circular microchannel. J Therm Anal Calorim. 2018;131:2843–63.

  13. 13.

    Toghraie D, Abdollah MMD, Pourfattah P, Akbari OA, Ruhani B. Numerical investigation of flow and heat transfer characteristics in smooth, sinusoidal and zigzag-shaped microchannel with and without nanofluid. J Therm Anal Calorim. 2018;131:1757–66.

  14. 14.

    Esfe MH, Arani AAA, Yan WM, Aghaie A, Afrand M, Sina N. Mixed convection of functionalized DWCNT/water nanofluid in baffled lid-driven cavities. Therm Sci. 2018;22(6):2503–14.

  15. 15.

    Esfe MH, Mahian O, Hajmohammad MH, Wongwises S. Design of a heat exchanger working with organic nanofluids using multi-objective particle swarm optimization algorithm and response surface method. Int J Heat Mass Transf. 2018;119:922–30.

  16. 16.

    Esfe MH, Nadooshan AA, Arshi A, Alirezaie A. Convective heat transfer and pressure drop of aqua based TiO2 nanofluids at different diameters of nanoparticles: data analysis and modeling with artificial neural network. Physica E. 2018;97:155–61.

  17. 17.

    Esfe MH, Rostamian H, Samghabadi AS, Arani AAA. Application of three-level general factorial design approach for thermal conductivity of MgO/water nanofluids. Appl Therm Eng. 2017;127:1194–9.

  18. 18.

    Esfe MH, Arani AAA, Yan WM, Aghaei A. Natural convection in T-shaped cavities filled with water-based suspensions of COOH-functionalized multi walled carbon nanotubes. Int J Mech Sci. 2017;121:21–32.

  19. 19.

    Esfe MH, Zabihi F, Rostamian H, Esfandeh S. Experimental investigation and model development of the non-Newtonian behavior of CuO-MWCNT-10w40 hybrid nano-lubricant for lubrication purposes. J Mol Liq. 2018;249:677–87.

  20. 20.

    Esfe MH, Arani AAA, Amani J, Wongwises S. Estimation of heat transfer coefficient and thermal performance factor of TiO2-water nanofluid using different thermal conductivity models. Curr Nano Sci. 2017;13(6):548–62.

  21. 21.

    Sarafraz MM, Arjomandi M. Thermal performance analysis of a microchannel heat sink cooling with copper oxide–indium (CuO/In) nano-suspensions at high-temperatures. Appl Therm Eng. 2018;137:700–9.

  22. 22.

    Sarafraz MM, Arjomandi M. Demonstration of plausible application of gallium nano-suspension in microchannel solar thermal receiver: experimental assessment of thermo-hydraulic performance of microchannel. Int Commun Heat Mass Transf. 2018;94:39–46.

  23. 23.

    Sarafraz MM, Arya H, Arjomandi M. Thermal and hydraulic analysis of a rectangular microchannel with gallium-copper oxide nano-suspension. J Mol Liq. 2018;263:382–9.

  24. 24.

    Sarafraz MM, Hart J, Shrestha E, Arya H, Arjomandi M. Experimental thermal energy assessment of a liquid metal eutectic in a microchannel heat exchanger equipped with a (10 Hz/50 Hz) resonator. Appl Therm Eng. 2019;148:578–90.

  25. 25.

    Valdevit L, Pantano A, Stone HA, Evans AG. Optimal active cooling performance of meltallic sandwich panels with prismatic cores. Int J Heat Mass Transf. 2006;49(21–22):3819–30.

  26. 26.

    Weerapun D, Somchai W. A comparison of the thermal and hydraulic performances between miniature pin fin heat sink and micro-channel heat sink with zigzag flow channel together with using nanofluids. Heat Mass Transf. 2018;54(11):3265–74.

  27. 27.

    Mehdi A, Mohammad G, Leila AK, Reza A. Effect of magnetic field on the forced convection heat transfer and pressure drop of a magnetic nanofluid in a miniature heat sink. Heat Mass Transf. 2015;51:953–64.

  28. 28.

    Lu TJ, Xu F, Wen T. Thermo-fluid behaviour of periodic cellular metals. Beijing: Science Press; 2010.

  29. 29.

    Liu JF. Theory and design for fin-tube heat exchangers. Ha Erbin: Harbin Institute of Technology Press; 2012.

  30. 30.

    Li XF, Li Y, Ding T. Engineering fluid mechanics. Beijing: China Water Power Press; 2009.

  31. 31.

    Chen LT. Study on heat transfer performance of directionally solidified porous copper microchannel heat sink. Ph.D. dissertation, Tsinghua University, Beijing; 2012.

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This work is a part of the author’s post-doctor study in Zhejiang University of Technology, Hangzhou, China.

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Correspondence to Tengwei Qiu.

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Qiu, T., Wen, D., Hong, W. et al. Heat transfer performance of a porous copper micro-channel heat sink. J Therm Anal Calorim 139, 1453–1462 (2020) doi:10.1007/s10973-019-08547-4

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  • Porous copper micro-channel
  • Heat sink
  • Heat dissipation model
  • Heat transfer performance