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MHD forced convection and entropy generation of CuO-water nanofluid in a microchannel considering slip velocity and temperature jump


Flow field, heat transfer and entropy generation of forced convection of CuO-water nanofluid is investigated in a parallel plate microchannel in the presence of magnetic field. Two vertical micromixers are attached on the hot walls of the microchannel. To consider the effect of the Brownian motion of the nanoparticles, the KKL model is utilized to estimate thermal conductivity of the nanofluid. The governing equations, which are accompanied with the slip velocity and temperature jump boundary conditions, are solved by the finite volume method (FVM) and SIMPLER algorithm. The study is conducted for the Reynolds numbers in the range of 10 < Re < 100, Hartmann numbers in the range of 0 < Ha < 40, Knudsen numbers ranging of 0 < Kn < 0.1 and volume fraction of nanoparticles ranging of 0 < φ < 0.04. The results show that when the Hartmann or Reynolds numbers, or the volume fraction of nanoparticles increase, the average Nusselt number and the total entropy generation rate increase. Furthermore, when Knudsen number increases, the total entropy generation rate decreases.

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a j :

Coefficient values of \(g^{\prime}\) function

B 0 :

Magnetic field intensity (N/m A)

c i :

Coefficients of fully developed velocity profile

c p :

Specific heat capacity (J/kg K)

d np :

Nanoparticles diameter (nm)

D h :

Hydraulic diameter (m)

h :

Local heat transfer coefficient (W/m2 K)


Hartmann number

k :

Thermal conductivity (W/m K)


Knudsen number

L :

Unit length (m)

n :

Unit normal vector


Nusselt number

p :

Pressure (N/m2)

P :

Dimensionless pressure


Poiseuille number (≡f Re)


Prandtl number


Reynolds number

R bf :

Thermal interfacial resistance (Km2/W)

\(\dot{s}^{\prime\prime\prime}\) :

Volumetric rate of entropy generation (W/m3 K)

\(\dot{S}^{\prime\prime\prime}\) :

Dimensionless volumetric rate of entropy generation

\(\dot{S}\) :

Dimensionless total rate of entropy generation

T :

Temperature (K)

(u,v) :

Velocity components (m/s)

(U,V) :

Dimensionless velocity components

(x,y) :

Coordinates (m)

(X,Y) :

Dimensionless coordinates

α :

Thermal diffusivity (m2/s)

γ :

Heat capacity ratio (≡ c p/c v)

θ :

Dimensionless temperature

κ b :

Boltzmann constant (=1.38064852 × 10−23 kg m2/s2 K)

λ :

Mean free path (m)

μ :

Dynamic viscosity (kg/m s)

ν :

Kinematic viscosity (m2/s)

ρ :

Density (kg/m3)

σ :

Electrical conductivity (1/Ω m = A2 s3/kg m3)

σ T :

Thermal accommodation coefficient

σ v :

Momentum accommodation coefficient

χ :

Irreversibility distribution ratio

\(\phi\) :

Nanoparticles volume fraction

0 :

Reference state value




Base fluid


Brownian motion component of thermal conductivity




Fully developed region

h :

Hot walls


Inlet flow






Static component of thermal conductivity

w :



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The authors wish to thank the Energy Research Institute of the University of Kashan for their support regarding this research (Grant No. 55806).

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Correspondence to Ahmad Ababaei.

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Technical Editor: Francis HR Franca.

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Abbaszadeh, M., Ababaei, A., Abbasian Arani, A.A. et al. MHD forced convection and entropy generation of CuO-water nanofluid in a microchannel considering slip velocity and temperature jump. J Braz. Soc. Mech. Sci. Eng. 39, 775–790 (2017).

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  • CuO-water nanofluid
  • Entropy generation
  • Parallel plate microchannel
  • Slip velocity and temperature jump
  • Magnetic field
  • KKL Brownian motion model