MHD natural convection of a CNT-based nanofluid-filled annular circular enclosure with inner heat-generating solid cylinder


The present work is dedicated to understanding the natural convective flow mechanism and heat exchange under magnetic field within a concentric circular annulus between a heat-generating conductive internal cylinder and an isothermally cold external cylinder filled with a CNTs-water-based nanoliquid. The free convective flow is generated by the temperature gradient created between the inner heat-generating solid cylinder and the outer cold cylinder. The flow equations in their dimensionless form are numerically solved via the technique of finite volume. The dependency of various factors and their interrelationships affecting the thermo-hydrodynamic behavior and heat exchange rate within the system has been delineated. The findings of this study emphasize the role of the considered control parameters with regards to the hydro-thermal characteristics and the heat exchange rate within the annulus.

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Data availability statement

This manuscript has associated data in a data repository. [Authors’ comment: The data that support the findings of this study are available from the corresponding author upon reasonable request.]


B 0 :

Magnetic field (N/A m2)

\(C_{p}\) :

Specific heat at constant pressure (J kg1 K1)

g :

Acceleration of gravity (m s−2)

k :

Heat conductivity (W m1 K1)

Kr :

Heat conductivity ratio (m2 s1)

p :

Pressure (N m2)

P :

Dimensionless pressure

Q 0 :

Volumetric heat generation (W m3)

r :

Radius (m)

RR :

The inner to outer radius ratio, RR = r2/r1

T :

Temperature (K)

u,v :

Components of velocity (m s1)

U, V :

Dimensionless of velocity components (m s1)

x, y :

Coordinate system (m)

X, Y :

Dimensionless of coordinates

\(\psi\) :

Stream function (m2 s1)

\(\Psi\) :

Dimensionless of stream function

α :

Thermal diffusivity (m2 s1)

\(\beta\) :

Coefficient of volume expansion (K1)

\(\mu\) :

Dynamic viscosity, kg m1 s1

\(\rho\) :

Density (kg m3)

\(\upsilon\) :

Kinematic viscosity (m2 s1)


Electrical conductivity (1/Ω m)

\(\phi\) :

CNTs concentration (in volume)

\(\theta\) :

Dimensionless temperature



c :


f :

Host liquid (pure water)

h :


nf :



Refer to the inner cylinder


Refer to the outer cylinder


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Correspondence to Ali J. Chamkha.

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Tayebi, T., Öztop, H.F. & Chamkha, A.J. MHD natural convection of a CNT-based nanofluid-filled annular circular enclosure with inner heat-generating solid cylinder. Eur. Phys. J. Plus 136, 150 (2021).

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