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


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.


Entropy generation Nanofluid Turbulent flow Rotating cylinder SST kω model 

List of symbols


Surface of domain (m2)


Boltzmann constant (–)


Specific heat (J kg−1 K−1)


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


Cylinder diameter (m)


Molecular diameter of base fluid (nm)


Nanoparticle diameter (nm)


Heat transfer coefficient (W m−2 K−1)


Turbulent kinetic energy(m−2 s−2)


Mean free path of water (–)


Non-dimensional thermal entropy generations (–)


Non-dimensional viscous entropy generations (–)


Mean non-dimensional entropy generation rate (–)


Nusselt number (–)


Pressure (Pa)


Prandtl number (–)


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)


Time (s)


Temperature (K)


Streamwise dimension of coordinates (m)


Cross-stream dimension of coordinates (m)


Streamwise velocity (m s−1)


Cross-stream velocity (m s−1)

ui, uj

Velocity components (m s−1)

Greek symbols


Free stream (–)


Volume fraction (–)


Angular displacement from the front stagnation point (°)


Fluid dynamic viscosity (kg m−1 s−1)


Fluid kinematic viscosity (m2 s−1)


Fluid density (kg m−3)


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


Thermal conductivity (W m−1 K−1)


Distance between particles (nm)


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)


Deviatoric stress tensor (kg m−1 s−2)









Base fluid


Particle, pressure








Wall, pure water



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


  1. 1.
    Kendoush AA. An approximate solution of the convective heat transfer from an isothermal rotating cylinder. Int J Heat Fluid Flow. 1996;17(4):439–41.CrossRefGoogle Scholar
  2. 2.
    Paramane SB, Sharma A. Numerical investigation of heat and fluid flow across a rotating circular cylinder maintained at constant temperature in 2-D laminar flow regime. Int J Heat Mass Transf. 2009;52(13):3205–16.CrossRefGoogle Scholar
  3. 3.
    Ma H, Zhou W, Lu X, Ding Z, Cao Y, Deng N, et al. Investigation on the air flow and heat transfer from a horizontal rotating cylinder. Int J Therm Sci. 2015;95:21–8.CrossRefGoogle Scholar
  4. 4.
    Shirejini SZ, Rashidi S, Esfahani J. Recovery of drop in heat transfer rate for a rotating system by nanofluids. J Mol Liq. 2016;220:961–9.CrossRefGoogle Scholar
  5. 5.
    Roslan R, Saleh H, Hashim I. Effect of rotating cylinder on heat transfer in a square enclosure filled with nanofluids. Int J Heat Mass Transf. 2012;55(23):7247–56.CrossRefGoogle Scholar
  6. 6.
    Turkyilmazoglu M. Nanofluid flow and heat transfer due to a rotating disk. Comput Fluids. 2014;94:139–46.CrossRefGoogle Scholar
  7. 7.
    Sheikholeslami M, Ganji D. Three dimensional heat and mass transfer in a rotating system using nanofluid. Powder Technol. 2014;253:789–96.CrossRefGoogle Scholar
  8. 8.
    Ellahi R, Hassan M, Zeeshan A. A study of heat transfer in power law nanofluid. Therm Sci. 2015;20(6):2015–26.CrossRefGoogle Scholar
  9. 9.
    Ellahi R, Hassan M, Zeeshan A, Khan AA. The shape effects of nanoparticles suspended in HFE-7100 over wedge with entropy generation and mixed convection. Appl Nanosci. 2016;6(5):641–51.CrossRefGoogle Scholar
  10. 10.
    Ellahi R, Hassan M, Zeeshan A. Aggregation effects on water base Al2O3-nanofluid over permeable wedge in mixed convection. Asia-Pac J Chem Eng. 2016;11(2):179–86.CrossRefGoogle Scholar
  11. 11.
    Rahman S, Ellahi R, Nadeem S, Zia QZ. Simultaneous effects of nanoparticles and slip on Jeffrey fluid through tapered artery with mild stenosis. J Mol Liq. 2016;218:484–93.CrossRefGoogle Scholar
  12. 12.
    Shehzad N, Zeeshan A, Ellahi R, Vafai K. Convective heat transfer of nanofluid in a wavy channel: Buongiorno’s mathematical model. J Mol Liq. 2016;222:446–55.CrossRefGoogle Scholar
  13. 13.
    Ellahi R, Ellahi R, Zeeshan A, Zeeshan A, Hassan M, Hassan M. Particle shape effects on Marangoni convection boundary layer flow of a nanofluid. Int J Numer Methods Heat Fluid Flow. 2016;26(7):2160–74.CrossRefGoogle Scholar
  14. 14.
    Bhatti MM, Zeeshan A, Ellahi R. Endoscope analysis on peristaltic blood flow of Sisko fluid with Titanium magneto-nanoparticles. Comput Biol Med. 2016;78:29–41.CrossRefGoogle Scholar
  15. 15.
    Sheikholeslami M, Zia Q, Ellahi R. Influence of induced magnetic field on free convection of nanofluid considering Koo-Kleinstreuer-Li (KKL) correlation. Appl Sci. 2016;6(11):324.CrossRefGoogle Scholar
  16. 16.
    Ellahi R, Zeeshan A, Hassan M. A study of Fe3O4 nanoparticles aggregation in engine oil base nanofluid over the vertical stretching of a permeable sheet in a mixed convection. J Zhejiang Univ Sci A. 2016.Google Scholar
  17. 17.
    Bhatti M, Zeeshan A, Ellahi R. Simultaneous effects of coagulation and variable magnetic field on peristaltically induced motion of Jeffrey nanofluid containing gyrotactic microorganism. Microvasc Res. 2017;110:32–42.CrossRefGoogle Scholar
  18. 18.
    Ellahi R, Tariq M, Hassan M, Vafai K. On boundary layer nano-ferroliquid flow under the influence of low oscillating stretchable rotating disk. J Mol Liq. 2017;229:339–45.CrossRefGoogle Scholar
  19. 19.
    Rashidi S, Esfahani JA, Ellahi R. Convective heat transfer and particle motion in an obstructed duct with two side by side obstacles by means of DPM model. Appl Sci. 2017;7(4):431.CrossRefGoogle Scholar
  20. 20.
    Hassan M, Zeeshan A, Majeed A, Ellahi R. Particle shape effects on ferrofuids flow and heat transfer under influence of low oscillating magnetic field. J Magn Magn Mater. 2017;443:36–44.CrossRefGoogle Scholar
  21. 21.
    Minea AA. Numerical studies on heat transfer enhancement in different closed enclosures heated symmetrically. J Therm Anal Calorim. 2015;121(2):711–20.CrossRefGoogle Scholar
  22. 22.
    Meibodi SS, Kianifar A, Mahian O, Wongwises S. Second law analysis of a nanofluid-based solar collector using experimental data. J Therm Anal Calorim. 2016;126(2):617–25.CrossRefGoogle Scholar
  23. 23.
    Bahiraei M. A numerical study of heat transfer characteristics of CuO–water nanofluid by Euler–Lagrange approach. J Therm Anal Calorim. 2016;123(2):1591–9.CrossRefGoogle Scholar
  24. 24.
    Pourfayaz F, Sanjarian N, Kasaeian A, Astaraei FR, Sameti M, Nasirivatan S. An experimental comparison of SiO2/water nanofluid heat transfer in square and circular cross-sectional channels. J Therm Anal Calorim. 2017. Scholar
  25. 25.
    Minea AA. Comparative study of turbulent heat transfer of nanofluids. J Therm Anal Calorim. 2016;124(1):407–16.CrossRefGoogle Scholar
  26. 26.
    Estellé P, Halelfadl S, Maré T. Thermophysical properties and heat transfer performance of carbon nanotubes water-based nanofluids. J Therm Anal Calorim. 2017;127(3):2075–81.CrossRefGoogle Scholar
  27. 27.
    Estellé P, Mahian O, Maré T, Öztop HF. Natural convection of CNT water-based nanofluids in a differentially heated square cavity. J Therm Anal Calorim. 2017;128(3):1765–70.CrossRefGoogle Scholar
  28. 28.
    Esfe MH, Behbahani PM, Arani AAA, Sarlak MR. Thermal conductivity enhancement of SiO2–MWCNT (85: 15%)–EG hybrid nanofluids. J Therm Anal Calorim. 2017;128(1):249–58.CrossRefGoogle Scholar
  29. 29.
    Esfahani J, Akbarzadeh M, Rashidi S, Rosen M, Ellahi R. Influences of wavy wall and nanoparticles on entropy generation over heat exchanger plat. Int J Heat Mass Transf. 2017;109:1162–71.CrossRefGoogle Scholar
  30. 30.
    A/K Abu-Hijleh B. Entropy generation in laminar convection from an isothermal cylinder in cross flow. Energy. 1998;23(10):851–7.CrossRefGoogle Scholar
  31. 31.
    Eger T, Bol T, Daróczy L, Janiga G, Schroth R, Thévenin D. Numerical investigations of entropy generation to analyze and improve heat transfer processes in electric machines. Int J Heat Mass Transf. 2016;102:1199–208.CrossRefGoogle Scholar
  32. 32.
    Parsazadeh M, Mohammed H, Fathinia F. Influence of nanofluid on turbulent forced convective flow in a channel with detached rib-arrays. Int Commun Heat Mass Transf. 2013;46:97–105.CrossRefGoogle Scholar
  33. 33.
    Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 1994;32(8):1598–605.CrossRefGoogle Scholar
  34. 34.
    Valipour MS, Masoodi R, Rashidi S, Bovand M, Mirhosseini M. A numerical study on convection around a square cylinder using Al2O3-H2O nanofluid. Therm Sci. 2014;18(4):1305–14.CrossRefGoogle Scholar
  35. 35.
    Zhou S-Q, Ni R. Measurement of the specific heat capacity of water-based Al2O3 nanofluid. Appl Phys Lett. 2008;92(9):093123.CrossRefGoogle Scholar
  36. 36.
    Masoumi N, Sohrabi N, Behzadmehr A. A new model for calculating the effective viscosity of nanofluids. J Phys D Appl Phys. 2009;42(5):055501.CrossRefGoogle Scholar
  37. 37.
    Chon CH, Kihm KD, Lee SP, Choi SU. Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement. Appl Phys Lett. 2005;87(15):153107.CrossRefGoogle Scholar
  38. 38.
    Patankar SV. Numerical heat transfer and fluid flow. New York: Hemisphere; 1980. p. 25–73.Google Scholar
  39. 39.
    Peller H, Lippig V, Straub D, Waibel R. Thermofluiddynamic experiments with a heated and rotating circular cylinder in crossflow. Exp Fluids. 1984;2(3):113–20.CrossRefGoogle Scholar

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

Personalised recommendations