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Numerical investigation of the effect of a porous block and flow injection using non-Newtonian nanofluid on heat transfer and entropy generation in a microchannel with hydrophobic walls

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Abstract

The microchannel cooling technology is an efficient procedure for dissipating heat from high-power devices. In this research, forced convective and entropy generation of a non-Newtonian fluid (water) with 1% and 3% volume fraction of nanoadditives (Al2O3) are investigated in a two-dimensional microchannel. Three configurations for microchannel are considered in this examination to investigate the effect of different Reynolds numbers of injection (25, 37.5, and 50), Darcy numbers (0.01, 0.005, and 0.001), and velocity boundary conditions (hydrophobic and superhydrophobic) on dimensionless velocity, dimensionless temperature, Nusselt number, and entropy generation. Microchannel in case A equipped with an injection in case B and both injection and the porous block in case C. The results show more relative Reynolds number and nanoparticle concentrations and less the Darcy number cause higher dimensionless velocity around the hot wall and the Nusselt number, which is beneficial. The same changes in velocity and temperature can be seen by applying superhydrophobic boundary conditions instead of hydrophobic due to less impact of the solid walls on the flow. The Nusselt number can be increased up to 128.86% in case C. Frictional entropy generation raises by the considerable amount of 461.62% in the presence of porous media. In comparison, this amount is just 133.47% for thermal entropy generation. However, entropy generation analysis shows thermal entropy generation is considerably more than frictional entropy generation; thus, it has a dominant role in calculating total entropy generation.

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Abbreviations

x :

Horizontal axis, m

y :

Vertical axis, m

L :

Microchannel length, m

h :

Microchannel height, m

u :

Horizontal velocity component, m/s

v :

Vertical velocity component, m/s

P :

Pressure, Pa

K :

Permeability, m2

K * :

Permeability of modified, m2

n :

Power-law factor

C F :

Inertia factor

T :

Temperature, K

k r :

Relative proportion of the porous media thermal conductivity to the thermal conductivity of nanofluid

X D :

Exergy losses, W

S :

Entropy generation rate, W/K

\(\dot{S}\) :

Local volumetric entropy generation, W/K m3

Nu:

Nusselt number

Pr:

Prandtl number

Da:

Darcy number

Re:

Reynolds number

D h :

Hydraulic diameter of microchannel = 2h, m

k :

Thermal conductivity, W/m K

C p :

Specific heat, J/kg K

H :

Dimensionless length of the microchannel

Y :

Dimensionless vertical axis

X :

Dimensionless horizontal axis

U :

Dimensionless horizontal velocity

V :

Dimensionless vertical velocity

\(\beta *\) :

No dimension of slip velocity coefficient

\(\mu *\) :

Consistency factor, Pa sn

\(\theta\) :

No dimension of temperature

\(\beta\) :

Slip velocity index

ε :

Porosity

φ :

Nanoparticle volume fraction

\(\gamma\) :

Shear rate

\(\rho\) :

Density, kg/m3

pp:

Porous particles

out:

Outlet

in:

Inlet

h:

Hot

c:

Cold

s:

Slip

f:

Fluid

fr:

Frictional

e:

Effective

t:

Thermal

np:

Nanoparticle

max:

Maximum

nf:

Nanofluid

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Kashan, Kashan, Iran

    Mohammad Derikvand

  2. Department of Mechanical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Mojtaba Shams Solari

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

    Davood Toghraie

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  1. Mohammad Derikvand
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  3. Davood Toghraie
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Derikvand, M., Solari, M.S. & Toghraie, D. Numerical investigation of the effect of a porous block and flow injection using non-Newtonian nanofluid on heat transfer and entropy generation in a microchannel with hydrophobic walls. Eur. Phys. J. Plus 136, 867 (2021). https://doi.org/10.1140/epjp/s13360-021-01846-6

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