Magnetic field effects on forced convection flow of a hybrid nanofluid in a cylinder filled with porous media: a numerical study


The magnetic field can serve as a proper controlling parameter for heat transfer and fluid flow; it can be also employed to maximize the thermodynamic efficiency in various fields. Nanofluids and porous inserts are among the conventional approaches of heat transfer enhancements. Porous media, in addition to improving the heat transfer, can enhance the pressure drop. This research presents a numerical investigation on the magnetohydrodynamics forced convection effects of Al2O3–CuO–water nanofluid inside a partitioned cylinder within a porous medium. The calculations were carried out for a broad range of governing parameters. The nanofluid flow is modeled as a two-phase flow using two-phase mixture model, and the Darcy–Brinkman–Forchheimer equation is employed to model fluid flow in porous media. Simulation was also conducted under the laminar flow regime by finite volume method. Furthermore, the thermal boundary condition of constant uniform heat flux was imposed on the cylinder walls. The average Nusselt number as well as the performance evaluation criteria (PEC) were examined for diverse Darcy numbers (0.0001 < Da < 0.1) and Hartmann numbers (0 < Ha < 40). The results indicate the significant impact of Hartmann and Darcy number enhancement on the elevation of heat transfer coefficient. Additionally, incorporation of nanoparticles to the base fluid increased the PEC in all cases. Moreover, the PEC reached to its maximum value in configurations involving permeable porous media (i.e., a medium with Da = 0.1 and Ha = 40).

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B :

Intensity of the magnetic field

C :

Specific heat/J kg−1 K−1

g :

Gravity acceleration/m s−2

J :

Electric current density

K :

Permeability of porous medium/m2

k :

Thermal conductivity/W m−1 K−1

L :


P :

Dimensionless pressure

p :



Heat flux/W m−2

R :


T :


U, V :

Dimensionless velocity

u, v :

Velocity components/m s−1

X, Y :

Dimensionless cylindrical coordinates

x, y :

Cylindrical coordinates/m

α :

Thermal diffusivity/m2 s−1

β :

Thermal expansion coefficient/K−1

ε :


θ :

Dimensionless temperature

ϑ :

Kinematic viscosity/m2 s−1

μ :

Dynamic viscosity/kg m−1 s−1

ρ :

Density/kg m3

σ :

Electrical conductivity/Ω−1 m−1

φ :

Volume fraction

ψ :

Magnetic field angle








Hybrid nanofluid




Computational fluid dynamics


Carbon nanotubes


Darcy number


Hartmann number




Nusselt number


Prandtl number


Performance evaluation criteria


Reynolds number


Semi-implicit method for pressure-linked equations


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Correspondence to Hamid Saffari.

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Aminian, E., Moghadasi, H. & Saffari, H. Magnetic field effects on forced convection flow of a hybrid nanofluid in a cylinder filled with porous media: a numerical study. J Therm Anal Calorim 141, 2019–2031 (2020).

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  • Forced convection
  • Nanofluid
  • MHD
  • Porous media
  • PEC