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Entropy generation of MHD nanofluid inside an inclined wavy cavity by lattice Boltzmann method

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Abstract

In this study, lattice Boltzmann method is applied in order to simulate the magnetohydrodynamic (MHD) natural convection heat transfer and entropy generation of CuO–water nanofluid inside an inclined wavy cavity. The left wavy wall is heated sinusoidal, while the right flat wall is kept at a constant temperature. The top and the bottom horizontal walls are smooth and insulated against heat and mass. The effects of active parameters such as solid volume fraction of nanoparticles, Rayleigh number, Hartmann number and inclination angles are examined on flow, heat transfer and entropy generation. The results proved that the heat transfer and entropy generation decline significantly with increasing Hartmann numbers, while those rise with increasing Rayleigh numbers. The results show that the effect of nanoparticles volume fraction on dimensionless Nusselt number and entropy generation is more pronounced at high Rayleigh number than at low Rayleigh number. Also the results indicate that the mean Nusselt number and total entropy generation changes with inclination angle, while the minimum values of \(Nu_{\text{m}}\) and S belong to \(\theta = \pi /3\) and 0, respectively.

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Abbreviations

\(B\) :

Magnetic field

\(Be\) :

Bejan number

\(c\) :

Lattice speed

\(C_{\text{S}}\) :

Speed of sound

\(C_{\text{P}}\) :

Heat capacity (J kg−1 K−1)

\(F\) :

External force

\({\text{f}}_{\text{i}}\) :

Particle distribution function

\({\text{g}}_{\text{i}}\) :

Energy distribution function

\(g\) :

Gravity (m s−2)

\(H\) :

Height of the cavity (m)

\(Ha\) :

Hartmann number

\(k\) :

Thermal conductivity (W m−1 K−1)

\(Nu\) :

Nusselt number

\(Pr = \frac{\vartheta }{\alpha }\) :

Prandtl number

\(Ra = \frac{{g_{y} \beta H^{3}\Delta T}}{\vartheta \alpha }\) :

Rayleigh number

\({\text{S}}\) :

Dimensionless entropy

\(S_{\text{HTI}}\) :

Entropy generation due to heat transfer

\(S_{\text{FFI}}\) :

Entropy generation due to fluid friction

\(S_{\text{MHFI}}\) :

Entropy generation due to magnetic field

\(u\) :

Velocity in the x-direction (m s−1)

\(v\) :

Velocity in the y-direction (m s−1)

\(U = \frac{uW}{{\alpha_{\text{f}} }}\) :

Dimensionless velocity in the x-direction

\(V = \frac{vW}{{\alpha_{\text{f}} }}\) :

Dimensionless velocity in the y-direction

\(W\) :

Length of the cavity (m)

\(x,y\) :

Coordinates (m)

\(\alpha\) :

Thermal diffusivity (m2 s−1)

\(\beta\) :

Thermal expansion coefficient (K−1)

\(\varphi\) :

Nanoparticles volume fraction

\(\phi\) :

Phase deviation

\(\mu\) :

Dynamic viscosity (kg m−1 s−1)

\(\rho\) :

Density (kg m−3)

\(\sigma\) :

Electrical conductivity

\(T^{*} = \frac{{T - T_{\text{C}} }}{{T_{\text{H}} - T_{\text{C}} }}\) :

Non-dimensional temperature

\(\tau\) :

Relaxation time

\({\text{eq}}\) :

Equilibrium state

f:

Fluid

l:

Local

m:

Mean

nf:

Nanofluid

p:

Nanoparticle

T:

Thermal

\(\vartheta\) :

Velocity

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Acknowledgements

The work of I. Pop was supported by the Grant PN-III-P4-ID-PCE-2016-0036, UEFISCDI, Romania. The authors wish to express their thanks to the very competent reviewers for the very good comments and suggestions.

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Authors and Affiliations

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

    Alireza Shahriari

  2. Department of Industrial, Mechanical and Aerospace Engineering, Buein Zahra Technical University, Buein Zahra, Qazvin, Islamic Republic of Iran

    Hamid Reza Ashorynejad

  3. Department of Mathematics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    Ioan Pop

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  1. Alireza Shahriari
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  3. Ioan Pop
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Correspondence to Ioan Pop.

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Shahriari, A., Ashorynejad, H.R. & Pop, I. Entropy generation of MHD nanofluid inside an inclined wavy cavity by lattice Boltzmann method. J Therm Anal Calorim 135, 283–303 (2019). https://doi.org/10.1007/s10973-018-7061-x

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