Optimal arrangements of a heat sink partially filled with multilayered porous media employing hybrid nanofluid

  • Hossein Arasteh
  • Ramin Mashayekhi
  • Davood ToghraieEmail author
  • Arash Karimipour
  • Mehdi Bahiraei
  • Alireza Rahbari


Although many studies have addressed the urge of exploring the porous media partially embedded in a channel due to its wide engineering applications, the heat transfer and fluid flow of a channel consisting of multilayered metal foam are relatively untouched. To tackle this research gap, a numerical study is conducted to analyze a channel partially filled with a three-layered porous medium—occupying sixty percent of a heat sink—over the Reynolds numbers ranging from 50 to 150 and water base fluid. To this aim, two configuration models of porous media are evaluated here: metal foam with (A) similar particle diameters (2 mm) and different porosities (0.75, 0.85, 0.95) and (B) similar porosities (0.88) and different particle diameters (1, 2, 3 mm). Darcy–Brinkman–Forchheimer and local thermal non-equilibrium methods are used to solve the momentum and energy equations in the porous region, respectively. The validity assessment of the local thermal equilibrium method elucidates that its accuracy is questionable at higher porosities and particle diameters of the metal foam—highlighting the necessity of incorporating the LTNE method under the mentioned circumstances. Among the considered geometries, the optimal arrangements of metal foam at both models are selected according to the performance evaluation criteria value.


Porous media Copper metal foam Multilayered Local thermal non-equilibrium Optimal arrangement Nanofluid Heat sink 

List of symbols


Area (m2)


Fluid to solid specific area


Specific heat capacity (J kg−1 K−1)


Particle diameter (m)


Darcy number


Friction coefficient


Friction coefficient of plain channel


Heat transfer coefficient (W m−2 K−1)


Channel height (m)


Porous thickness (m)


Fluid to solid heat transfer coefficient


Permeability (m2)


Thermal conductivity (W m−1 K−1)


Effective thermal conductivity (W m−1 K−1)


Effective thermal conductivity of porous region solid phase (W m−1 K−1)


Effective thermal conductivity of porous region fluid phase (W m−1 K−1)


Ratio of effective solid thermal conductivity to that of fluid


Length of the channel (m)


Nusselt number


Nusselt number of plain channel


Local Nusselt number


Average Nusselt number


Performance evaluation criteria


Pressure (Pa)


Prandtl number


Heat flux (w m−2)


Reynolds number


Temperature (K)


x-direction velocity (m s−1)


y-direction velocity (m s−1)

Greek symbols


Dimensionless temperature


Cinematic viscosity (m2 s−1)


Dynamic viscosity (kg ms−1)


Density (kg m−3)




Volume fractions of nanoparticles













Solid phase of porous region





  1. 1.
    Ghazvini M, Shokouhmand H. Investigation of a nanofluid-cooled microchannel heat sink using fin and porous media approaches. Energy Convers Manag. 2009;50:2373–80.CrossRefGoogle Scholar
  2. 2.
    Esfe MH, Ahangar MRH, Toghraie D, Hajmohammad MH, Rostamian H, Tourang H. Designing artificial neural network on thermal conductivity of Al2O3–water–EG (60–40%) nanofluid using experimental data. J Therm Anal Calorim. 2016;126:837–843.CrossRefGoogle Scholar
  3. 3.
    Rezaei O, Akbari OA, Marzban A, Toghraie D, Pourfattah F, Mashayekhi R. The numerical investigation of heat transfer and pressure drop of turbulent flow in a triangular microchannel. Phys. E. 2017;93:179–189.CrossRefGoogle Scholar
  4. 4.
    Najafi Amel A, Kouravand S, Zarafshan P, Kermani AM, Khashehchi M. Study the heat recovery performance of micro and nano metfoam regenerators in alpha type stirling engine conditions. Nanoscale Microscale Thermophys Eng. 2018;22:137–51.CrossRefGoogle Scholar
  5. 5.
    Tana WC, Sawa LH, Thiama HS, Xuanb J, Caic Z, Yewa MCh. Overview of porous media/metal foam application in fuel cells and solar power systems. Renew Sustain Energy Rev. 2018;96:181–97.CrossRefGoogle Scholar
  6. 6.
    Saedodina S, Zamzamianb SAH, Eshah Nimvaric M, Wongwisesd S, Javaniyan Jouybaria H. Performance evaluation of a flat-plate solar collector filled with porous metal foam: experimental and numerical analysis. Energy Convers Manag. 2017;153:278–87.CrossRefGoogle Scholar
  7. 7.
    Mahian O, Kianifar A, Kalogirou SA, Pop I, Wongwises S. A review of the applications of nanofluids in solar energy. Int J Heat Mass Transf. 2013;57:582–94.CrossRefGoogle Scholar
  8. 8.
    Bamorovat Abadi Gh, Kim KCh. Experimental heat transfer and pressure drop in a metal-foam-filled tube heat exchanger. Exp Therm Fluid Sci. 2017;82:42–9.CrossRefGoogle Scholar
  9. 9.
    Heydari M, Toghraie D, Akbari OA. The effect of semi-attached and offset mid-truncated ribs and Water/TiO2 nanofluid on flow and heat transfer properties in a triangular microchannel. Therm Sci and Eng Prog. 2017;2:140–150.CrossRefGoogle Scholar
  10. 10.
    Lu W, Zhang T, Yang M, Wub Y. Analytical solutions of force convective heat transfer in plate heat exchangers partially filled with metal foams. Int J Heat Mass Transf. 2017;110:476–81.CrossRefGoogle Scholar
  11. 11.
    Shen B, Yan H, Sunden B, Xue H, Xie G. Forced convection and heat transfer of water-cooled microchannel heat sinks with various structured metal foams. Int J Heat Mass Transf. 2017;113:1043–53.CrossRefGoogle Scholar
  12. 12.
    Khashan SA, Al-Amiri AM, Al-Nimr MA. Assessment of the local thermal non-equilibrium condition in developing forced convection flows through fluid-saturated porous tubes. Appl Therm Eng. 2005;25:1429–45.CrossRefGoogle Scholar
  13. 13.
    Zhang X, Liu W. New criterion for local thermal equilibrium in porous media. J Thermophys Heat Transf. 2008;4:649–53.CrossRefGoogle Scholar
  14. 14.
    Al-Sumaily GF, Sheridan J, Thompson MC. Validation of thermal equilibrium assumption in forced convection steady and pulsatile flows over a cylinder embedded in a porous channel. Int Commun Heat Mass Transf. 2013;43:30–8.CrossRefGoogle Scholar
  15. 15.
    Dehghan M, Tajik Jamal-Abad M, Rashidi S. Analytical interpretation of the local thermal non-equilibrium condition of porous media imbedded in tube heat exchangers. Energy Convers Manag. 2014;85:264–71.CrossRefGoogle Scholar
  16. 16.
    Xu HJ, Qu ZG, Tao WQ. Numerical investigation on self-coupling heat transfer in a counterflow double-pipe heat exchanger filled with metallic foams. Appl Therm Eng. 2014;66:43–54.CrossRefGoogle Scholar
  17. 17.
    Xu HJ, Gong L, Zhao CY, Yang YH, Xu ZG. Analytical considerations of local thermal non-equilibrium conditions for thermal transport in metal foams. Int J Therm Sci. 2015;95:73–87.CrossRefGoogle Scholar
  18. 18.
    Lin W, Xie G, Yuan J, Sundén B. Comparison and analysis of heat transfer in aluminum foam using local thermal equilibrium or nonequilibrium model. Heat Transf Eng. 2015;37:314–22.CrossRefGoogle Scholar
  19. 19.
    Shokouhmand H, Jam F, Salimpour MR. Optimal porosity in an air heater conduit filled with a porous matrix. Heat Transf Eng. 2009;30:375–82.CrossRefGoogle Scholar
  20. 20.
    Xu HJ, Qu ZG, Tao WQ. Analytical solution of forced convective heat transfer in tubes partially filled with metallic foam using the two-equation model. Int J Heat Mass Transf. 2011;54:3846–55.CrossRefGoogle Scholar
  21. 21.
    Hung TC, Huang YX, Yan WM. Thermal performance of porous microchannel heat sink: effects of enlarging channel outlet. Int Commun Heat Mass Transf. 2013;48:86–92.CrossRefGoogle Scholar
  22. 22.
    Mahmoudi Y, Karimi N. Numerical investigation of heat transfer enhancement in a pipe partially filled with a porous material under local thermal non-equilibrium condition. Int J Heat Mass Transf. 2014;68:161–73.CrossRefGoogle Scholar
  23. 23.
    Dathathri S, Balaji C. Heat transfer and optimization studies on layered porous stackings under an imposed pressure drop. Int Commun Heat Mass Transf. 2015;60:32–6.CrossRefGoogle Scholar
  24. 24.
    Chuan L, Wang XD, Wang TH, Yan WM. Fluid flow and heat transfer in microchannel heat sink based on porous fin design concept. Int Commun Heat Mass Transf. 2015;65:52–7.CrossRefGoogle Scholar
  25. 25.
    Wang ShL, Li XY, Wang XD, Lu G. Flow and heat transfer characteristics in double-layered microchannel heat sinks with porous fins. Int Commun Heat Mass Transf. 2018;93:41–7.CrossRefGoogle Scholar
  26. 26.
    Shenoy M, Sheremet I. Pop, Convective Flow and Heat Transfer from wavy Surfaces: viscous Fluids, Porous Media and Nanofluids. New York: CRC Press, Taylor & Francis Group; 2016.CrossRefGoogle Scholar
  27. 27.
    Kasaeian A, Azarian RD, Mahian O, Lioua K, Chamkha AJ, Wongwises S, Pop I. Nanofluid flow and heat transfer in porous media: a review of the latest developments. Int J Heat Mass Transf. 2017;107:778–91.CrossRefGoogle Scholar
  28. 28.
    Mahian O, Kolsi L, Amani M, Estelle P, Ahmadi G, kleinstreuer C, Marshal JS, Siavashi M, Taylor RA, Niazmand H, Wangwises S, Hayat T, Kolanjiyil A, Kasaeian A, and Pop I. Recent advances in modeling and simulation of nanofluid flows-part I: fundamentals and theory. Phys Rep. 2018. Scholar
  29. 29.
    Mahian O, Kolsi L, Amani M, Estelle P, Ahmadi G, kleinstreuer C, Marshal JS, Taylor RA, Abu-Nada A, Rashidi S, Niazmand H, Wangwises S, Hayat T, Kolanjiyil A, Kasaeian A, and Pop I. Recent advances in modeling and simulation of nanofluid flows-part II: applications. Phys Rep. 2018. Scholar
  30. 30.
    Khanfar Kh, Vafai K. Applications of nanofluid in porous medium. J Therm Anal Calorim. 2018. Scholar
  31. 31.
    Vafai K. Handbook of porous media. 3rd ed. Boca Raton: CRC Press; 2015.Google Scholar
  32. 32.
    Merrikh AA, Mohamad AA. Non-Darcy effects in buoyancy driven flows in an enclosure filled with vertically layered porous media. Int J Heat Mass Transf. 2002;45:4305–13.CrossRefGoogle Scholar
  33. 33.
    Prommas R. Theoretical and experimental study of heat and mass transfer mechanism during convective drying of multi-layered porous packed bed. Int Commun Heat Mass Transf. 2011;38:900–5.CrossRefGoogle Scholar
  34. 34.
    Tyvand PA, Storesletten L. onset of convection in an anisotropic porous layer with vertical principal axes. Transp Porous Media. 2015;108:581–93.CrossRefGoogle Scholar
  35. 35.
    Siavashi M, Talesh Bahrami HR, Aminian E. Optimization of heat transfer enhancement and pumping power of a heat exchanger tube using gradient and multi-layered porous foams. Appl Therm Eng. 2018;138:465–74.CrossRefGoogle Scholar
  36. 36.
    Nield DA, Bejan A. Convection in porous media. 4th ed. New York: Springer; 2013.CrossRefGoogle Scholar
  37. 37.
    Alazmi B, Vafai K. Analysis of variants within the porous media transport models. ASME J Heat Transf. 1999;122:303–26.CrossRefGoogle Scholar
  38. 38.
    Yarmand H, Gharehkhani S, Seyed Shirazi SF, Goodarzi M, Amiri A, Sarsama WS, Alehashem MS, Dahari M, Kazi SN. Study of synthesis, stability and thermo-physical properties of graphene nanoplatelet/platinum hybrid nanofluid. Int Commun Heat Mass Transf. 2016;77:15–21.CrossRefGoogle Scholar
  39. 39.
    Khodabandeh E, Bahiraei M, Mashayekhi R, Talebjedi B, Toghraie D. Thermal performance of Ag–water nanofluid in tube equipped with novel conical strip inserts using two-phase method: geometry effects and particle migration considerations. Powder Technol. 2018;338:87–100.CrossRefGoogle Scholar
  40. 40.
    Dabiri S, Khodabandeh E, Khoeini Poorfar A, Mashayekhi R, Toghraie D, Abadian Zade SA. Parametric investigation of thermal characteristic in trapezoidal cavity receiver for a linear Fresnel solar collector concentrator. Energy. 2018;153:17–26.CrossRefGoogle Scholar
  41. 41.
    Heydari A, Akbari OA, Safaei MR, Derakhshani M, AAA Alrashed A, Mashayekhi R, Ahmadi Sheikh Shabani Gh, Zarringhalam M, Nguyen TKh. The effect of attack angle of triangular ribs on heat transfer of nanofluids in a microchannel. J Therm Anal Calorim. 2018;131:2893–912.CrossRefGoogle Scholar
  42. 42.
    Bahiraei M, Rahmani R, Yaghoobi A, Khodabandeh E, Mashayekhi R, Amani M. Recent research contributions concerning use of nanofluids in heat exchangers: a critical review. Appl Therm Eng. 2018;133:137–59.CrossRefGoogle Scholar
  43. 43.
    Mashayekhi R, Khodabandeh E, Akbari OA, Toghraie D, Bahiraei M, Gholami M. CFD analysis of thermal and hydrodynamic characteristics of hybrid nanofluid in a new designed sinusoidal double-layered microchannel heat sink. J Therm Anal Calorim. 2018;134:2305–15.CrossRefGoogle Scholar
  44. 44.
    Kim D, Kwon Y, Cho Y, Li Ch, Cheong S, Hwang Y, Lee J, Hong D, Moon S. Convective heat transfer characteristics of nanofluids under laminar and turbulent flow conditions. J Curr Appl Phys. 2009;9:119–23.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIsfahan University of TechnologyIsfahanIran
  2. 2.Young Researchers and Elite Club, Khomeinishahr BranchIslamic Azad UniversityKhomeinishahrIran
  3. 3.Department of Mechanical Engineering, Khomeinishahr BranchIslamic Azad UniversityKhomeinishahrIran
  4. 4.Department of Mechanical Engineering, Najafabad BranchIslamic Azad UniversityNajafabadIran
  5. 5.Department of Mechanical EngineeringKermanshah University of TechnologyKermanshahIran
  6. 6.Research School of EngineeringThe Australian National UniversityCanberraAustralia

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