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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 70, 2016 - Issue 11
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Original Articles

Numerical simulations of transitional and turbulent natural convection in laterally heated cylindrical enclosures for crystal growth

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Pages 1195-1212 | Received 16 Dec 2015, Accepted 13 Jul 2016, Published online: 28 Nov 2016
 

ABSTRACT

The present numerical work, the first of its kind, aims at establishing the threshold parameters for dynamic similitude (based on the Rayleigh number (Ra)), for free convection in a cylindrical enclosure heated laterally. Ra considered in this study spanned a range between 750 and 8.8 × 108, where the characteristic length, L, used in its definition is represented by the ratio of cylindrical enclosure’s volume to its lateral surface area. The commercial code, ANSYS FLUENT, is used to model a 2-D axisymmetric cylindrical geometry. When comparatively analyzed, the results allowed conclusions associating values of the Ra with flow development from laminar to turbulent.

Nomenclature

Dω=

cross-diffusion term

g=

gravity

Gr=

Grashof number

k=

turbulence kinetic energy

L=

characteristic length (volume/lateral area)

p=

pressure

Pk=

generation of turbulence kinetic energy

Pω=

generation of ω

Pr=

Prandtl number

R=

radius of the enclosure

Ra=

Rayleigh number

t=

time

T=

temperature

vr=

radial velocity

vz=

axial velocity

Yk=

dissipation of k

Yω=

dissipation of ω

α=

thermal diffusivity

αT=

turbulent thermal diffusivity

β=

thermal expansion coefficient

μ=

dynamic viscosity

μT=

eddy viscosity

ν=

kinematic viscosity

ρ=

density

τ=

shear stress

ω=

specific dissipation rate

Nomenclature

Dω=

cross-diffusion term

g=

gravity

Gr=

Grashof number

k=

turbulence kinetic energy

L=

characteristic length (volume/lateral area)

p=

pressure

Pk=

generation of turbulence kinetic energy

Pω=

generation of ω

Pr=

Prandtl number

R=

radius of the enclosure

Ra=

Rayleigh number

t=

time

T=

temperature

vr=

radial velocity

vz=

axial velocity

Yk=

dissipation of k

Yω=

dissipation of ω

α=

thermal diffusivity

αT=

turbulent thermal diffusivity

β=

thermal expansion coefficient

μ=

dynamic viscosity

μT=

eddy viscosity

ν=

kinematic viscosity

ρ=

density

τ=

shear stress

ω=

specific dissipation rate

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