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Journal of Thermal Analysis and Calorimetry

, Volume 133, Issue 2, pp 1061–1073 | Cite as

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

  • Milad Shirazi
  • Alireza Shateri
  • Morteza Bayareh
Article

Abstract

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.

Keywords

Mixed convection heat transfer Nanofluid Eccentricity Nusselt number Rayleigh number Richardson number 

List of symbols

Cp

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

Greek letters

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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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Milad Shirazi
    • 1
  • Alireza Shateri
    • 1
  • Morteza Bayareh
    • 1
  1. 1.Department of Mechanical EngineeringShahrekord UniversityShahrekordIran

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