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Journal of Thermal Analysis and Calorimetry

, Volume 132, Issue 2, pp 1189–1200 | Cite as

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

  • Shima Akar
  • Saman Rashidi
  • Javad Abolfazli Esfahani
Article

Abstract

This paper performs an entropy generation analysis for nanofluid turbulent flow around a rotating cylinder. A finite volume method based on SST kω 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.

Keywords

Entropy generation Nanofluid Turbulent flow Rotating cylinder SST kω model 

List of symbols

A

Surface of domain (m2)

Bc

Boltzmann constant (–)

C

Specific heat (J kg−1 K−1)

Cp

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

D

Cylinder diameter (m)

df

Molecular diameter of base fluid (nm)

dp

Nanoparticle diameter (nm)

h

Heat transfer coefficient (W m−2 K−1)

k

Turbulent kinetic energy(m−2 s−2)

lBF

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)

ui, uj

Velocity components (m s−1)

Greek symbols

\(\infty\)

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)

τij

Deviatoric stress tensor (kg m−1 s−2)

Subscripts

ave

Average

B

Brownian

eff

Effective

f

Base fluid

p

Particle, pressure

s

Solid

T

Turbulent

v

Viscous

w

Wall, pure water

Notes

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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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  • Shima Akar
    • 1
  • Saman Rashidi
    • 2
  • Javad Abolfazli Esfahani
    • 1
  1. 1.Department of Mechanical EngineeringFerdowsi University of MashhadMashhadIran
  2. 2.Department of Mechanical Engineering, Semnan BranchIslamic Azad UniversitySemnanIran

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