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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 |
| = | 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 |
| = | 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 |