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Heat and Mass Transfer

, 46:15 | Cite as

Numerical investigation of natural convection of Al2O3 nanofluid in vertical annuli

  • Omid AboualiEmail author
  • Ahmad Falahatpisheh
Original

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.

Keywords

Nusselt Number Natural Convection Free Convection Particle Fraction Base Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

A

Aspect ratio H/L

A

Area

B

Constant of Kapitza resistance

C

Constant in Nusselt numbers ratio

C1

Constant in thermal conductivity model

cp

Specific heat (J/kg K)

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

Random motion velocity of nanoparticles

D

Diameter

D0

Diffusion coefficient

g

Gravity acceleration (m/s2)

GrL

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

H

Height of annulus

K

Radius ratio of annulus

kb

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

Greek symbols

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)

Subscript

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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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentShiraz UniversityShirazIran
  2. 2.Mechanical Engineering DepartmentUniversity of South CarolinaColumbiaUSA

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