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Second law of thermodynamic analysis for nanofluid turbulent flow around a rotating cylinder

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Abstract

This paper performs an entropy generation analysis for nanofluid turbulent flow around a rotating cylinder. A finite volume method based on SST k–ω turbulence model is employed to solve the governing equations and calculate the viscous and thermal entropy generations. The effects of different parameters containing the non-dimensional rotation rate, nanoparticle concentration, and Reynolds number on the viscous and thermal entropy generations and Bejan number are investigated. The obtained results indicate that there is an optimal non-dimensional rotation ratio at α = 1.5 as it has the minimal viscous entropy generation among other values of α. The viscous entropy generation seems to be enveloped around the cylinder. Finally, the viscous entropy generation is dominant in most of the domain except at the regions with an upward drift and a thin layer around the cylinder wall.

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Abbreviations

A :

Surface of domain (m2)

B c :

Boltzmann constant (–)

C :

Specific heat (J kg−1 K−1)

C p :

Specific heat at constant pressure (J kg−1 K−1)

D :

Cylinder diameter (m)

d f :

Molecular diameter of base fluid (nm)

d p :

Nanoparticle diameter (nm)

h :

Heat transfer coefficient (W m−2 K−1)

k :

Turbulent kinetic energy(m−2 s−2)

l BF :

Mean free path of water (–)

\(N_{\text{g,thermal}}\) :

Non-dimensional thermal entropy generations (–)

\(N_{\text{g,viscous}}\) :

Non-dimensional viscous entropy generations (–)

N :

Mean non-dimensional entropy generation rate (–)

Nu :

Nusselt number (–)

p :

Pressure (Pa)

Pr :

Prandtl number (–)

Re :

Flow Reynolds number (–)

\(S_{\text{g,thermal}}^{{{\prime \prime \prime }}}\) :

Thermal entropy generation rate (W m−3 K−1)

\(S_{\text{g,viscous}}^{{{\prime \prime \prime }}}\) :

Viscous entropy generation rate (W m−3 K−1)

t :

Time (s)

T :

Temperature (K)

x :

Streamwise dimension of coordinates (m)

y :

Cross-stream dimension of coordinates (m)

u :

Streamwise velocity (m s−1)

v :

Cross-stream velocity (m s−1)

u i, u j :

Velocity components (m s−1)

\(\infty\) :

Free stream (–)

φ :

Volume fraction (–)

θ :

Angular displacement from the front stagnation point (°)

μ :

Fluid dynamic viscosity (kg m−1 s−1)

υ :

Fluid kinematic viscosity (m2 s−1)

ρ :

Fluid density (kg m−3)

α :

Thermal diffusivity of fluid (m2 s−1), non-dimensional rotation rate (–)

λ :

Thermal conductivity (W m−1 K−1)

δ :

Distance between particles (nm)

ω :

Angular velocity of the rotating cylinder (rad s−1), specific rate of dissipation (s−1)

\(\Gamma _{\text{k}}\) :

Effective diffusivity of k (m s−2)

\(\Gamma _{\text{w}}\) :

Effective diffusivity of ω (m s−2)

τ ij :

Deviatoric stress tensor (kg m−1 s−2)

ave:

Average

B:

Brownian

eff:

Effective

f:

Base fluid

p:

Particle, pressure

s:

Solid

T:

Turbulent

v:

Viscous

w:

Wall, pure water

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Acknowledgements

This research was supported by the Office of the Vice Chancellor for Research, Ferdowsi University of Mashhad, under Grant No. 43872.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, 91775-1111, Iran

    Shima Akar & Javad Abolfazli Esfahani

  2. Department of Mechanical Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran

    Saman Rashidi

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  1. Shima Akar
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Correspondence to Javad Abolfazli Esfahani.

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Akar, S., Rashidi, S. & Esfahani, J.A. Second law of thermodynamic analysis for nanofluid turbulent flow around a rotating cylinder. J Therm Anal Calorim 132, 1189–1200 (2018). https://doi.org/10.1007/s10973-017-6907-y

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  • DOI: https://doi.org/10.1007/s10973-017-6907-y

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