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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 70, 2016 - Issue 10
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Original Articles

Free convection enhancement in an annulus between horizontal confocal elliptical cylinders using hybrid nanofluids

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Pages 1141-1156 | Received 13 Apr 2016, Accepted 09 Aug 2016, Published online: 20 Oct 2016
 

ABSTRACT

In the present paper, natural convection in an annulus between two confocal elliptic cylinders filled with a Cu-Al2O3/water hybrid nanofluid is investigated numerically. The inner cylinder is heated at a constant surface temperature while the outer wall is isothermally cooled. The basic equations are formulated in elliptic coordinates and developed in terms of the vorticity-stream function formulation using the dimensionless form for 2D, laminar and incompressible flow under steady-state condition. The governing equations are discretized using the finite volume method and solved by an in-house FORTRAN code. Numerical simulations are performed for various volume fractions of nanoparticles (0 ≤ ϕ ≤ 0.12) and Rayleigh numbers (103 ≤ Ra ≤ 3 × 105). The eccentricity of the inner and outer ellipses and the angle of orientation are fixed at e1 = 0.9, e2 = 0.6 and γ = 0° respectively. It is found that employing a Cu-Al2O3/water hybrid nanofluid is more efficient in heat transfer rate compared to the similar Al2O3/water nanofluid.

Nomenclature

A1, A2=

major axes of the inner and outer elliptic cylinders (m)

B1, B2=

minor axes of the inner and outer elliptic cylinders (m)

Cp=

specific heat at constant pressure (J · kg−1 · K−1)

g=

gravitational acceleration (m · s−2)

h=

metric coefficient (m)

H=

dimensionless h

K=

thermal conductivity (W · m−1 · K−1)

Nu=

Nusselt number

Pr=

Prandtl number

Ra=

Rayleigh number

T=

dimension temperature (K)

u, v=

axial and radial velocities (m · s−1)

Vη, Vθ=

velocity components in η, θ directions (m · s−1)

x, y=

Cartesian coordinates (m)

α=

thermal diffusivity (m2 · s−1)

β=

thermal expansion coefficient (K−1)

γ=

orientation angle of the annulus

K=

thermal conductivity (W · m−1 · K−1)

μ=

dynamic viscosity, kg/m s

υ=

kinematic viscosity (m2 · s−1)

ρ=

density (kg · m−3)

ϕ=

volume fraction of the nanoparticles

η, θ=

elliptic coordinates, (m)

ψ=

stream function (m2 · s−1)

ω=

vorticity (s−1)

e1, e2=

eccentricities of ellipses

Subscripts=
c=

cold

h=

hot

f=

fluid

hnf=

hybrid nanofluid

nf=

nanofluid

p=

solid particles

1=

inner cylinder

2=

outer cylinder

Superscript=
*=

dimensionless parameters

Nomenclature

A1, A2=

major axes of the inner and outer elliptic cylinders (m)

B1, B2=

minor axes of the inner and outer elliptic cylinders (m)

Cp=

specific heat at constant pressure (J · kg−1 · K−1)

g=

gravitational acceleration (m · s−2)

h=

metric coefficient (m)

H=

dimensionless h

K=

thermal conductivity (W · m−1 · K−1)

Nu=

Nusselt number

Pr=

Prandtl number

Ra=

Rayleigh number

T=

dimension temperature (K)

u, v=

axial and radial velocities (m · s−1)

Vη, Vθ=

velocity components in η, θ directions (m · s−1)

x, y=

Cartesian coordinates (m)

α=

thermal diffusivity (m2 · s−1)

β=

thermal expansion coefficient (K−1)

γ=

orientation angle of the annulus

K=

thermal conductivity (W · m−1 · K−1)

μ=

dynamic viscosity, kg/m s

υ=

kinematic viscosity (m2 · s−1)

ρ=

density (kg · m−3)

ϕ=

volume fraction of the nanoparticles

η, θ=

elliptic coordinates, (m)

ψ=

stream function (m2 · s−1)

ω=

vorticity (s−1)

e1, e2=

eccentricities of ellipses

Subscripts=
c=

cold

h=

hot

f=

fluid

hnf=

hybrid nanofluid

nf=

nanofluid

p=

solid particles

1=

inner cylinder

2=

outer cylinder

Superscript=
*=

dimensionless parameters

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