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Numerical investigation of natural convection of Al2O3 nanofluid in vertical annuli

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Abstract

This paper presents the numerical study of internal free convection of Al2O3 water nanofluid in vertical annuli. Vertical walls are maintained at constant temperatures and horizontal walls are adiabatic. Results are validated by experimental data. Effect of nanofluids on natural convection is investigated as a function of geometrical and physical parameters and particle fractions for aspect ratio of 1 ≤ H/L ≤ 5, Grashof number of 103 ≤ Gr ≤ 105 and concentration of 0 ≤ ϕ ≤ 0.06. More than 330 different numerical cases are investigated to develop a new correlation for the Nusselt number. This correlation is presented as a function of Nusselt number of base fluid and particle fraction which is a linear decreasing function of particle fraction. The developed correlation for annuli is also valid for the natural convection of Al2O3 water nanofluid in a square cavity. Furthermore, the effect of the viscosity and conductivity models on the Nusselt number of nanofluids in cylindrical cavities are discussed.

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Abbreviations

A :

Aspect ratio H/L

A :

Area

B :

Constant of Kapitza resistance

C :

Constant in Nusselt numbers ratio

C 1 :

Constant in thermal conductivity model

c p :

Specific heat (J/kg K)

\( \bar{C}_{{{\text{R}}.{\text{M}}}} \) :

Random motion velocity of nanoparticles

D :

Diameter

D 0 :

Diffusion coefficient

g :

Gravity acceleration (m/s2)

Gr L :

Grashof number \( g\beta_{\text{f}} \Updelta TL^{3} /\nu_{\text{f}}^{2} \)

H :

Height of annulus

K :

Radius ratio of annulus

k b :

Boltzmann constant 1.3807 × 10−23 J/K

k :

Thermal conductivity (W/m K)

L :

Gap (r o − r i)

l :

Mean free path

p :

Static pressure (Pa)

Pr :

Prandtl number ν f/α f

Q :

Heat flux (W)

\( Re_{{d_{\text{nano}} }} \) :

Reynolds number based on particle diameter

Ra :

Rayleigh number = Gr L·Pr

r :

Radius

T :

Temperature (°C) or (K)

V :

Velocity

X, r :

Axial and radial coordinate

α :

Thermal diffusivity (m2/s)

β :

Volumetric thermal expansion coefficient (1/K)

ϕ :

Nanoparticle fraction

μ :

Dynamic viscosity (kg/m s)

ν :

Kinematic viscosity (m2/s)

θ :

Non dimensional temperature

ρ :

Density (kg/m3)

bf:

Base fluid

C:

Cold

eff:

Effective property

f:

Properties at film temperature

H:

Hot

i:

Inner

nf:

Nanofluid

o:

Outer

Particle:

Nanofluid particle

R.M:

Random motion

r:

Radial component

x:

Axial coordinate

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Authors and Affiliations

  1. Mechanical Engineering Department, Shiraz University, Shiraz, Iran

    Omid Abouali

  2. Mechanical Engineering Department, University of South Carolina, Columbia, SC, USA

    Ahmad Falahatpisheh

Authors
  1. Omid Abouali
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  2. Ahmad Falahatpisheh
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Correspondence to Omid Abouali.

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Abouali, O., Falahatpisheh, A. Numerical investigation of natural convection of Al2O3 nanofluid in vertical annuli. Heat Mass Transfer 46, 15–23 (2009). https://doi.org/10.1007/s00231-009-0540-7

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