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ABSTRACT
This work qualifies and quantifies the natural convective phenomena occurring in a hemispherical enclosure filled with ZnO-Water monophasic nanofluid with a volume fraction varying between 0% (pure water) and 10%. The dome of the cavity is kept isothermal while its circular base generates a power varying between 0.5W and 400W. The disc can be inclined with respect to the horizontal plane by an angle varying between 0 and 180° (horizontal disk with a dome facing upwards and downwards respectively). The 3D numerical approach is carried out with the finite volume method based on the SIMPLE algorithm. The temperature and velocity distributions are presented and the convective heat transfer is examined for all processed configurations. The nanofluidic convective heat transfer is quantified by means of correlations of the Nusselt-Rayleigh-Prandtl-tilt angle type. They allow to optimize the thermal design of these cavities used in the field of electronics.
Nomenclature
| a | = | thermal diffusivity (m2s−1) |
| b | = | exponent defined in Eq. (9), (-) |
| C | = | specific heat at constant pressure (J.kg−1K−1) |
| = | dimensionless unit vector opposite to the gravity direction | |
| g | = | gravity acceleration (m.s−2) |
| h | = | local convective heat transfer coefficient (Wm−2K−1) |
| = | average convective heat transfer coefficient (Wm−2K−1) | |
| k | = | coefficient defined in Eq. (9) |
| m | = | coefficient defined in Eq. (9) |
| N | = | number of disk surface elements (-) |
| Nu | = | local Nusselt Number (-) |
| = | average Nusselt Number (-) | |
| P | = | generated power (W) |
| Pr | = | Prandtl Number (-) |
| q | = | generated heat flux, |
| R | = | radius of the dome (m) |
| Ra | = | Rayleigh number (-) |
| = | ith element exchange area (m2) | |
| = | exchange area of the disk (m2) | |
| T | = | temperature (K) |
| = | temperature of the dome and initial temperature in the calculation process (K) | |
| = | dimensionless temperature (-) | |
| u | = | velocity (ms−1) |
| = | maximum u value (ms−1) | |
| = | dimensionless velocity, | |
| (x, y, z) | = | Cartesian coordinates (m) |
| Greek symbols | = | |
| α | = | inclination angle with respect to the horizontal plane (°) |
| β | = | volumetric expansion coefficient (K−1) |
| φ | = | volume fraction (-) |
| λ | = | thermal conductivity (Wm−1K−1) |
| μ | = | dynamic viscosity (Pa.s) |
| ρ | = | density (kg.m−3) |
| Subscripts | = | |
| f | = | base fluid (pure water) |
| nf | = | nanofluid |
| s | = | solid nanoparticles |
Nomenclature
| a | = | thermal diffusivity (m2s−1) |
| b | = | exponent defined in Eq. (9), (-) |
| C | = | specific heat at constant pressure (J.kg−1K−1) |
| = | dimensionless unit vector opposite to the gravity direction | |
| g | = | gravity acceleration (m.s−2) |
| h | = | local convective heat transfer coefficient (Wm−2K−1) |
| = | average convective heat transfer coefficient (Wm−2K−1) | |
| k | = | coefficient defined in Eq. (9) |
| m | = | coefficient defined in Eq. (9) |
| N | = | number of disk surface elements (-) |
| Nu | = | local Nusselt Number (-) |
| = | average Nusselt Number (-) | |
| P | = | generated power (W) |
| Pr | = | Prandtl Number (-) |
| q | = | generated heat flux, |
| R | = | radius of the dome (m) |
| Ra | = | Rayleigh number (-) |
| = | ith element exchange area (m2) | |
| = | exchange area of the disk (m2) | |
| T | = | temperature (K) |
| = | temperature of the dome and initial temperature in the calculation process (K) | |
| = | dimensionless temperature (-) | |
| u | = | velocity (ms−1) |
| = | maximum u value (ms−1) | |
| = | dimensionless velocity, | |
| (x, y, z) | = | Cartesian coordinates (m) |
| Greek symbols | = | |
| α | = | inclination angle with respect to the horizontal plane (°) |
| β | = | volumetric expansion coefficient (K−1) |
| φ | = | volume fraction (-) |
| λ | = | thermal conductivity (Wm−1K−1) |
| μ | = | dynamic viscosity (Pa.s) |
| ρ | = | density (kg.m−3) |
| Subscripts | = | |
| f | = | base fluid (pure water) |
| nf | = | nanofluid |
| s | = | solid nanoparticles |
Ackowledgements
Authors are grateful to Ania and Iken Baïri for their help.