Magnetohydrodynamic natural convection and entropy generation analyses inside a nanofluid-filled incinerator-shaped porous cavity with wavy heater block

  • M. Hashemi-TilehnoeeEmail author
  • A. S. Dogonchi
  • Seyyed Masoud Seyyedi
  • Ali J. Chamkha
  • D. D. Ganji


The aim of the current study is natural convection analysis conjugated with entropy generation analysis in an incinerator shaped permeable enclosure loaded with Al2O3–H2O nanofluid subjected to the magnetic field with a rectangular wavy heater block positioned on the bottom of the cavity wall. The bottom and top horizontal walls are adiabatic; the inclined and vertical walls are thought to be cooled. Firstly, the governing expressions and standard kε turbulence model are rewritten from dimensional form to non-dimensional form using dimensionless parameters such as vorticity and stream function. In the next step, the equation of entropy generation is written in dimensionless form. Then, the system of non-dimensional governing equations is solved by the finite volume method (FVM) conjugated with a non-dimensionalization scheme using ANSYS Fluent. Fine grids (wall y+ < 2) with inflated layers have been used for the higher Rayleigh number. The effects of the Rayleigh number in the laminar region (Ra = 103, 104, and 105) and turbulent region (Ra = 108, 0.5 × 109, and 109), Darcy number (Da = 0.01 and 100), Hartmann number (Ha = 0 and 40), and the nanoparticles (\( \phi = 2{{\% }} \)) on the entropy generation number and natural convection are investigated. The validation results were in good agreement with those of the literature. The results demonstrate that for the laminar region, the Nusselt number and entropy generation number increase as the Rayleigh number and the Darcy number grow, whereas both of them abate as Hartmann number increases. In the turbulent region, the average Nusselt number decreases by ascending the Darcy number. Also, for turbulent region (Ra = 109), convection flow strength decreases 6.28% when Hartmann number increases from 0 to 40, whereas the entropy generation number increases 31.5% at Da = 0.01.


Turbulent natural convection Nanofluid Entropy generation Porous media MHD ANSYS fluent 

List of symbols


Magnetic field strength


Magnetic field (T)


Bejan number


Specific heat capacity (J kg−1 K−1)


Dimensionless dissipation rate of turbulent kinetic energy


Gravitational acceleration (m s−2)


Hartmann number


Dimensional turbulent kinetic energy (m2 s−2)


Thermal conductivity (W m−1 K−1)


Dimensionless turbulent kinetic energy


Permeability of the medium (m2)


Length of the cavity (m)


Shape factor of nanoparticles


Entropy generation number


Nusselt number


Pressure (N m−2)


Prandtl number (–)


Rayleigh number


Rate of entropy generation per unit volume (J s−1 K−1 m−3)


Temperature (K)

u, v

Dimensional x and y components of velocity (m s−1)

x, y

Dimensional coordinates (m)

X, Y

Dimensionless coordinates

Greek letters


Thermal diffusivity (m2 s−1)


Thermal expansion coefficient (K−1)


Turbulent dissipation of kinetic energy (m2 s−3)


Dimensionless temperature (–)


Inclination angle (°)


Dynamic viscosity (N s m−2)


Kinematic viscosity (m2 s−1)


Density (kg m−3)


Electrical conductivity (Ω m−1)


\({k} - {\varepsilon}\) Turbulent model parameters


Cavity inclination angle (°)


Temperature difference


Volume fraction


Irreversibility distribution ratio


Dimensional stream function (m2 s−1)

\({{\Psi }}\)

Dimensionless stream function


Dimensional vorticity (s−1)

\({{\Omega }}\)

Dimensionless vorticity





Fluid friction






Heat transfer


Magnetic field




Porous medium







This work has been supported by a research contract of the Islamic Azad University, Aliabad Katoul Branch, Iran.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2020

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Aliabad Katoul BranchIslamic Azad UniversityAliabad KatoulIran
  2. 2.Mechanical Engineering Department, Prince Sultan Endowment for Energy and EnvironmentPrince Mohammad Bin Fahd UniversityAl-KhobarSaudi Arabia
  3. 3.RAK Research and Innovation CenterAmerican University of Ras Al KhaimahRas al-KhaimahUnited Arab Emirates
  4. 4.Department of Mechanical EngineeringBabol University of TechnologyBabolIran

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