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Numerical investigation of mixed convection heat transfer of a nanofluid in a circular enclosure with a rotating inner cylinder

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In the present paper, mixed convection heat transfer of water–Al2O3 nanofluid in the space between two cylinders is investigated numerically. The inner and outer cylinders are at Tc and Th temperatures, respectively. The forced and free convective heat transfers are due to the internal cylinder rotation and temperature difference between the two cylindrical surfaces, respectively. The effect of dimensionless parameters such as Rayleigh and Richardson numbers, the volume fraction of nanofluid, the eccentricity ratio and its angle on heat transfer ratio is analyzed. The governing equations are solved using a finite-difference method and SIMPLE algorithm. The results show that at eccentricity of ε = 0.0 and 0.5 and within the entire range of Rayleigh number 103 ≤ Ra ≤ 105 and Richardson number 0.1 ≤ Ri ≤ 100, an increase in Rayleigh and Richardson numbers leads to an increase in average Nusselt number on the inner cylinder wall. But at eccentricity of ε = 0.9, the average Nusselt number on the inner cylinder wall decreases with these dimensionless parameters. It is found that an increase in the volume fraction of the nanofluid results in an increase in average Nusselt number on the inner cylinder wall.

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C p :

Specific heat capacity at constant (J Kg−1 K−1)

D :

Cylinder diameter (m)

g :

Gravitational acceleration (m s−2)

Gr :

Grashof number

K :

Heat conductivity coefficient (W m−1 k−1)

L :

Specific length (m)

Nu :

Local Nusselt number

P :

Dimensionless pressure

Pe :

Péclet number

Pr :

Prandtl number

Q :

Heat transfer rate

r :

Radial coordinate

R :

Dimensionless radial coordinate

Ra :

Rayleigh number

Re :

Reynolds number

Ri :

Richardson number

RR :

Radial ratio

T :

Wall temperature (K)

u :

Velocity in radial direction (m s−1)

v :

Velocity in perimeter direction (m s−1)

U :

Dimensionless velocity in radial direction

V :

Dimensionless velocity in perimeter direction

α :

Heat diffusion coefficient (m2 s−1)

β :

Thermal diffusion coefficient (k−1)

ε :

Dimensionless eccentricity

ϕ :

Angular coordinate

φ :

Volume fraction of nanofluid

ν :

Kinematic viscosity (m2 s−1)

μ :

Dynamic viscosity (kg m−1 s−1)

ω :

Angular velocity (rad s−1)

ρ :

Density (kg m−3)

θ :

Dimensionless temperature


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Correspondence to Alireza Shateri.

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Shirazi, M., Shateri, A. & Bayareh, M. Numerical investigation of mixed convection heat transfer of a nanofluid in a circular enclosure with a rotating inner cylinder. J Therm Anal Calorim 133, 1061–1073 (2018).

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