A numerical investigation on the influence of nanoadditive shape on the natural convection and entropy generation inside a rectangle-shaped finned concentric annulus filled with boehmite alumina nanofluid using two-phase mixture model

  • Amin Shahsavar
  • Milad Rashidi
  • Mostafa Monfared Mosghani
  • Davood Toghraie
  • Pouyan TalebizadehsardariEmail author


The goal of this work is to numerically study the hydrothermal and entropy generation specifications of boehmite alumina (γ-AlOOH) nanofluid flowing in a finned concentric annulus using the two-phase mixture model. Different shapes for the nanoadditives are examined including cylindrical, brick, blade, platelet and spherical. The impacts of nanoadditive shape and volume concentration \((\varphi )\), Rayleigh number \(({\text{Ra}})\) and application of fins on the streamlines, isotherms, Nusselt number as well as both the local and global rates of entropy generation due to the heat transfer and fluid friction are examined. The results indicated that the addition of fins and employing a higher \({\text{Ra}}\) and \(\varphi\) cause a higher average Nusselt number and generation rate of thermal entropy. Moreover, it was found that, except for \({\text{Ra}} = 10^{3}\), the generation rate of frictional entropy intensifies by utilizing fins. Moreover, the frictional entropy generation rate was enhanced using a higher \({\text{Ra}}\) and \(\varphi\). The results depicted that the impact of fins on the Nusselt number and entropy generation is not varied by the nanoadditive shape and concentration. Furthermore, it was concluded that the best nanoadditive shape is cylindrical and platelet, respectively, based on the first and the second laws of thermodynamics.


Boehmite alumina nanofluid Nanoadditive shape Finned concentric annulus Natural convection Entropy generation 

List of symbols


Specific heat (J kg−1 K−1)


Diameter (m)


Drag coefficient


Acceleration of gravity (m s−2)


Average convection coefficient of inner wall (W m−2 K−1)


Rate of generation of turbulent kinetic energy (kg m−1 s−3)


Turbulent kinetic energy (m2 s−2)


Average Nusselt number of inner wall


Pressure (Pa)


Heat transfer rate (W)


Rayleigh number


Local entropy generation rate due to fluid friction (W m−3 K−1)


Local entropy generation rate due to heat transfer (W m−3 K−1)


Local total entropy generation rate (W m−3 K−1)


Global entropy generation rate due to fluid friction (W m−3 K−1)


Global entropy generation rate due to heat transfer (W m−3 K−1)


Global total entropy generation rate (W m−3 K−1)


Temperature (K)


Drift velocity (m s−1)


Mixture velocity (m s−1)


Relative velocity between a particle and fluid (m s−1)

Greek symbols


Turbulent dissipation rate (m2 s−3)


Thermal conductivity (W m−1 K−1)


Viscosity (kg m−1 s−1)


Turbulent viscosity (kg m−1 s−1)


Density (kg m−3)


Volume concentration





Base fluid




Inner wall




Outer wall





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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringKermanshah University of TechnologyKermanshahIran
  2. 2.Malek Ashtar University of TechnologyShirazIran
  3. 3.Department of Mechanical Engineering, Khomeinishahr BranchIslamic Azad UniversityKhomeinishahrIran
  4. 4.Department for Management of Science and Technology DevelopmentTon Duc Thang UniversityHo Chi Minh CityVietnam
  5. 5.Faculty of Applied SciencesTon Duc Thang UniversityHo Chi Minh CityVietnam

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