Heat and fluid flow analysis of metal foam embedded in a double-layered sinusoidal heat sink under local thermal non-equilibrium condition using nanofluid

  • Hossein Arasteh
  • Ramin Mashayekhi
  • Marjan GoodarziEmail author
  • S. Hossein Motaharpour
  • Mahidzal Dahari
  • Davood Toghraie


The present study aims to enhance the hydrothermal performance of a porous sinusoidal double-layered heat sink using nanofluid. The optimum thickness of metal foam (nickel) for different Reynolds numbers ranging from 10 to 100 for the laminar regime and Darcy numbers ranging from 10−4 to 10−2 is obtained. At the optimum porous thicknesses, nanofluid (silver–water) with three volume fractions of nanoparticles equal to 2, 3, and 4% is employed to enhance the heat sink thermal performance. Darcy–Brinkman–Forchheimer model and the local thermal non-equilibrium model or two equations method are employed to model the momentum equation and energy equations in the porous region, respectively. It was found that in the cases of Darcy numbers 10−4, 10−3, and 10−2 the dimensionless optimum porous thicknesses are 0.8, 0.8, and 0.2, respectively. It was also obtained that the maximum PEC number is 2.12 and it corresponds to the case with Darcy number 10−2, Reynolds number 40, and volume fraction of nanoparticles 0.04. The validity of local thermal equilibrium (LTE) assumption was investigated, and it was found that increasing the Darcy number which results in an enhancement in porous particle diameter leads to some errors in results, under LTE condition.


Porous medium Metal foam Local thermal non-equilibrium Nanofluid Double-layered channel Sinusoidal channel 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) \((k_{\text{ef}} = \varepsilon k_{\text{f}} )\)


Effective thermal conductivity of porous region fluid phase (W m−1 K−1) \(\left( {k_{\text{es}} = \left( {1 - \varepsilon } \right)k_{\text{s}} } \right)\)


Length of the steel plate (m)


Nusselt number


Nusselt number of plain channel


Local Nusselt number


Average Nusselt number


Pressure (Pa)


Performance evaluation criteria


Peclet number


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


Kinematic viscosity (m2 s−1)


Dynamic viscosity (kg m−1 s−1)


Density (kg m−3)




Volume fractions of nanoparticles







Downer channel












Porous medium solid phase


Nanofluid solid phase


Upper channel




Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.


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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.Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour SafetyTon Duc Thang UniversityHo Chi Minh CityVietnam
  4. 4.Department of Electrical Engineering, Faculty of EngineeringUniversity of MalayaKuala LumpurMalaysia
  5. 5.Department of Mechanical Engineering, Khomeinishahr BranchIslamic Azad UniversityKhomeinishahrIran

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