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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

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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.

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Abbreviations

A :

Area (m2)

a sf :

Fluid to solid specific area

C :

Specific heat capacity (J kg−1 K−1)

d p :

Particle diameter (m)

Da :

Darcy number

f :

Friction coefficient

f p :

Friction coefficient of plain channel

h :

Heat transfer coefficient (W m−2 K−1)

h c :

Channel height (m)

h p :

Porous thickness (m)

h sf :

Fluid to solid heat transfer coefficient

K :

Permeability (m2)

k :

Thermal conductivity (W m−1 K−1)

k eff :

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

k ef :

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

k es :

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

Nu p :

Nusselt number of plain channel

Nu x :

Local Nusselt number

Nu ave :

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)

\(\theta\) :

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

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

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Authors and Affiliations

  1. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

    Hossein Arasteh

  2. Young Researchers and Elite Club, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

    Ramin Mashayekhi & S. Hossein Motaharpour

  3. Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Marjan Goodarzi

  4. Department of Electrical Engineering, Faculty of Engineering, University of Malaya, Kuala Lumpur, Malaysia

    Mahidzal Dahari

  5. Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

    Davood Toghraie

Authors
  1. Hossein Arasteh
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Correspondence to Marjan Goodarzi.

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Arasteh, H., Mashayekhi, R., Goodarzi, M. et al. Heat and fluid flow analysis of metal foam embedded in a double-layered sinusoidal heat sink under local thermal non-equilibrium condition using nanofluid. J Therm Anal Calorim 138, 1461–1476 (2019). https://doi.org/10.1007/s10973-019-08168-x

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