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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
Article
  • 32 Downloads

Abstract

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.

Keywords

Porous medium Metal foam Local thermal non-equilibrium Nanofluid Double-layered channel Sinusoidal channel Heat sink 

List of symbols

A

Area (m2)

asf

Fluid to solid specific area

C

Specific heat capacity (J kg−1 K−1)

dp

Particle diameter (m)

Da

Darcy number

f

Friction coefficient

fp

Friction coefficient of plain channel

h

Heat transfer coefficient (W m−2 K−1)

hc

Channel height (m)

hp

Porous thickness (m)

hsf

Fluid to solid heat transfer coefficient

K

Permeability (m2)

k

Thermal conductivity (W m−1 K−1)

keff

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

kef

Effective thermal conductivity of porous region solid phase (W m−1 K−1) \((k_{\text{ef}} = \varepsilon k_{\text{f}} )\)

kes

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

l

Length of the steel plate (m)

Nu

Nusselt number

Nup

Nusselt number of plain channel

Nux

Local Nusselt number

Nuave

Average Nusselt number

p

Pressure (Pa)

PEC

Performance evaluation criteria

Pe

Peclet number

Pr

Prandtl number

q″

Heat flux (w m−2)

Re

Reynolds number

T

Temperature (K)

u

x-direction velocity (m s−1)

v

y-direction velocity (m s−1)

Greek symbols

\(\theta\)

Dimensionless temperature

\(\vartheta\)

Kinematic viscosity (m2 s−1)

\(\mu\)

Dynamic viscosity (kg m−1 s−1)

\(\rho\)

Density (kg m−3)

ε

Porosity

ϕ

Volume fractions of nanoparticles

Subscripts

b

Bulk

c

Channel

d

Downer channel

eff

Effective

f

Fluid

i

Inlet

o

Outlet

s

Solid

sp

Porous medium solid phase

sn

Nanofluid solid phase

u

Upper channel

w

Wall

Notes

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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