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Numerical analysis of mixed convection of two-phase non-Newtonian nanofluid flow inside a partially porous square enclosure with a rotating cylinder

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In this study, mixed convection heat transfer of the non-Newtonian power-law nanofluid including CuO nanoparticles, inside a partially porous square enclosure with a concentric rotating cylinder and a hot side wall is numerically investigated. Two-phase mixture model is utilized for nanofluid flow simulation and the mixture viscosity and thermal conductivity are computed by Corcione’s correlation. The effect of different angular velocity (− 4000 ≤ Ω ≤ 4000) for various Rayleigh (104 ≤ Ra ≤ 106), Darcy (10−4 ≤ Da ≤ 10−1), power-law index (0.8 ≤ n ≥ 1.2) and effective to base fluid thermal conductivity ratio (keff/kf= 16, 4) are studied on heat transfer. Results are presented and compared in terms of the average Nusselt number, and streamline and isotherm contours. Outcomes show that for different kinds of fluid, depending on the value of Ra, Da, keff/kf and the amount and direction of angular velocity, heat transfer can be improved by augmenting heat convection and also can be deteriorated by increasing viscosity. Consequently, optimal values of Ra, Da, keff/kf and Ω exist in order to maximize the average Nu number.

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C :

Consistency index (Nsn m−2)

C p :

Specific heat (J kg−1 K−1)

d p :

Diameter of the nanoparticle (m)

Da :

Darcy number

D ij :

Rate of deformation tensor

f drag :

Drag friction

g :

Gravitational acceleration (ms−2)

Κ :

Permeability of porous medium (m2)

k :

Thermal conductivity (W m−1 K−1)

k b :

Boltzmann constant (J K−1)

n :

Power-law index

Nu :

Nusselt number

P :

Pressure (Pa)

Pr :

Prandtl number

Ra :

Rayleigh number

Re :

Reynolds number

S gen,T :

Thermal entropy generation rate (W m−3 K−1)

T 0 :

Bulk temperature (K)








Base fluid








Solid medium



μ :

Dynamic viscosity (kg m−1s−1)

ρ :

Density (kg m−3)


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Correspondence to Qingang Xiong or Mohammad Hossein Doranehgard.

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Siavashi, M., Karimi, K., Xiong, Q. et al. Numerical analysis of mixed convection of two-phase non-Newtonian nanofluid flow inside a partially porous square enclosure with a rotating cylinder. J Therm Anal Calorim 137, 267–287 (2019).

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