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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 70, 2016 - Issue 3
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Original Articles

Natural convection and entropy generation in a cubical cavity with twin adiabatic blocks filled by aluminum oxide–water nanofluid

, , , &
Pages 242-259 | Received 18 Dec 2015, Accepted 23 Feb 2016, Published online: 20 Jul 2016
 

ABSTRACT

A finite volume-based three-dimensional numerical simulation on natural convection and entropy generation in a cubical cavity filled with a nanofluid of aluminum oxide–water is presented by vorticity–vector potential formalism. The blocks are adiabatic and the vertical walls are differentially heated unidirectionally. The variables considered are Ra, volumetric fraction of aluminum oxide particles, and block size. The results for fluid flow with a single-phase model are elucidated with iso-surfaces of temperature, Nusselt number, and Bejan number. The local entropy generated was due to friction surges when the volumetric fraction of nanoparticles was increased. The average Nusselt number rose with the increase in Ra and volumetric fraction of solid particles and declined with the increase in block size.

1. Nomenclature

Be=

Bejan number

Cp=

Specific heat at constant pressure (J/kgK)

g=

Gravitational acceleration (m/s2)

k=

Thermal conductivity (W/mK)

L=

Enclosure width

Lb=

Adiabatic block width

n=

Unit vector normal to the wall

Ns=

Dimensionless locally generated entropy

Nu=

Local Nusselt number

Pr=

Prandtl number

Ra=

Rayleigh number

Rc=

Thermal conductivity ratio (ks/kf)

S'gen=

Generated entropy (kJ/kgK)

t=

Dimensionless time (t′α/l2)

T=

Dimensionless temperature

Tc'=

Cold temperature (K)

Th=

Hot temperature (K)

To=

Bulk temperature (K)

=

Dimensionless velocity vector ()

x, y, z=

Dimensionless Cartesian coordinates (x′/l, y′/l, z′/l)

1.1.=

Greek Symbols

α=

Thermal diffusivity (m2/s)

β=

Thermal expansion coefficient (1 / K)

μ=

Dynamic viscosity (kg/ms)

ν=

Kinematic viscosity (m2/s)

=

Dimensionless vorticity ()

φ=

Volumetric fraction of nanoparticles

φS=

Irreversibility coefficient

=

Dimensionless vector potential ()

ρ=

Density (kg/m3)

ΔT=

Dimensionless temperature difference

1.2.=

Superscript

=

Dimensional variable

1.3.=

Subscripts

x, y, z=

Cartesian coordinates

fr=

Friction

f=

Fluid

av=

Average

nf=

Nanofluid

s=

Solid

th=

Thermal

tot=

Total

1. Nomenclature

Be=

Bejan number

Cp=

Specific heat at constant pressure (J/kgK)

g=

Gravitational acceleration (m/s2)

k=

Thermal conductivity (W/mK)

L=

Enclosure width

Lb=

Adiabatic block width

n=

Unit vector normal to the wall

Ns=

Dimensionless locally generated entropy

Nu=

Local Nusselt number

Pr=

Prandtl number

Ra=

Rayleigh number

Rc=

Thermal conductivity ratio (ks/kf)

S'gen=

Generated entropy (kJ/kgK)

t=

Dimensionless time (t′α/l2)

T=

Dimensionless temperature

Tc'=

Cold temperature (K)

Th=

Hot temperature (K)

To=

Bulk temperature (K)

=

Dimensionless velocity vector ()

x, y, z=

Dimensionless Cartesian coordinates (x′/l, y′/l, z′/l)

1.1.=

Greek Symbols

α=

Thermal diffusivity (m2/s)

β=

Thermal expansion coefficient (1 / K)

μ=

Dynamic viscosity (kg/ms)

ν=

Kinematic viscosity (m2/s)

=

Dimensionless vorticity ()

φ=

Volumetric fraction of nanoparticles

φS=

Irreversibility coefficient

=

Dimensionless vector potential ()

ρ=

Density (kg/m3)

ΔT=

Dimensionless temperature difference

1.2.=

Superscript

=

Dimensional variable

1.3.=

Subscripts

x, y, z=

Cartesian coordinates

fr=

Friction

f=

Fluid

av=

Average

nf=

Nanofluid

s=

Solid

th=

Thermal

tot=

Total

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