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ABSTRACT
In this study, the laminar natural convection flow inside a water-filled cavity with differentially heated vertical walls is investigated experimentally and numerically. Both of the walls are heated and cooled by two special heat exchangers that are attached to the walls and the rest are insulated. The main purpose of each test is to reach a uniform constant temperature on both of the heated and cooled walls. Early tests for an air-filled cavity showed that a uniform temperature on the walls is feasible, while a different trend was observed for a water-filled cavity with a nonuniform distribution of temperature. ANSYS FLUENT 15 employed four approaches in terms of boundary conditions for computational purposes. None of the three-dimensional (3D) and two-dimensional (2D) models of the cavity with a uniform wall temperature (the wall average temperature from the experiment) were suitable for predicting the Nusselt number. Therefore, it was essential to use the full model to properly predict the real distribution of temperature and Nusselt number on the walls. The 3D model of the cavity with a nonuniform wall temperature, which was borrowed from the experiment, also provided good results for the Nusselt number, but a measured temperature was still needed from the experiments. The 2D simulation's findings showed a weakness in properly capturing the streamlines for all ranges of Rayleigh numbers.
| Nomenclature | ||
| cp | = | specific heat (J/kg.K) |
| 3DF,2DF,3DC,3DCFFFF | = | thermal boundary condition explained in the manuscript |
| g | = | Gravity (m/s2) |
| Gk, Gb | = | generation of turbulence kinetic energy (kg.m/s3) |
| k | = | thermal conductivity (W/m.K) |
| L | = | characteristic length (m) |
| = | mass flow (kg/s) | |
| = | average Nusselt number | |
| P | = | pressure (Pa) |
| q″ | = | heat flux (W/m2) |
| Q | = | heat transfer (W) |
| R2 | = | R-squared value |
| Ra | = | Rayleigh number |
| Sk | = | kinetic energy source term (kg.m/s3) |
| Sϵ | = | dissipation rate source term (kg.m/s3) |
| T | = | temperature (K) |
| T′ | = | fluctuating temperature (K) |
| u′ | = | fluctuating velocity (m/s) |
| u | = | velocity (m/s) |
| = | time-averaged velocity (m/s) | |
| xi | = | coordinate |
| X | = | X-axis |
| Y | = | Y-axis |
| Ym | = | fluctuating dilatation (kg.m/s3) |
| y+ | = | dimensionless wall distance |
| Z | = | Z-axis |
| Greek symbols | ||
| α | = | thermal diffusivity (m2/s) |
| β | = | thermal expansion coefficient (1/K) |
| κ | = | turbulent kinetic energy (m2/s2) |
| ϵ | = | turbulent dissipation rate (m2/s3) |
| μ | = | dynamic viscosity (kg/m.s) |
| μt | = | turbulent viscosity (kg/m.s) |
| ν | = | kinematic viscosity(m2/s2) |
| ρ | = | density (kg/m3) |
| σϵ, σk | = | turbulent Prandtl numbers |
| Subscripts | ||
| c | = | cold wall |
| c-ave | = | average on the cold wall |
| c-wall | = | local wall temperature |
| h | = | hot wall |
| h-ave | = | average on the hot wall |
| h-wall | = | local wall temperature |
| in | = | pipe inlet |
| out | = | pipe outlet |
Additional information
Notes on contributors
Mostafa Mahdavi
Mostafa Mahdavi is a Ph.D. candidate in the Department of Mechanical and Aeronautical Engineering at the University of Pretoria. He received his master's degree from Shiraz University in Iran. His research interests include heat and mass transfer, natural and force convection, turbulence, convective nanofluids, particle migration and multiphase flow modelling.
Mohsen Sharifpur
Mohsen Sharifpur is a senior lecturer in the Department of Mechanical and Aeronautical Engineering at the University of Pretoria and is responsible for the Nanofluids Research Laboratory. He received a B.Sc. (Mechanical Engineering) degree from Shiraz University in Iran. He completed an M.Sc. degree in Nuclear Engineering and received a full scholarship for his Ph.D. study in Mechanical Engineering (Thermal Fluid) from the Eastern Mediterranean University. He is the author and co-author of more than 70 articles and conference papers. His research interests include convective multiphase flow, the thermal fluid behaviour of nanofluids, convection nanofluids, convection in porous media, computational fluid dynamics and waste heat in thermal systems.
Hadi Ghodsinezhad
Hadi Ghodsinezhad is currently completing his master's degree in Mechanical Engineering in the Department of Mechanical and Aeronautical Engineering at the University of Pretoria, South Africa. He obtained a B.Eng. degree in Mechanical Engineering at Urmia University, Iran, and a B.Eng. honours degree in Mechanical Engineering at the University of Pretoria in 2014.
Josua P. Meyer
Josua P. Meyer obtained his B.Eng. degree cum laude in 1984, an M.Eng. degree cum laude in 1986 and a Ph.D. in 1988, all in Mechanical Engineering from the University of Pretoria. He is registered as a professional engineer. Presently, he is the Chair of the School of Engineering at the University of Pretoria. He specialises in heat transfer, fluid mechanics and the thermodynamic aspects of heating, ventilation and air-conditioning. He is the author and co-author of more than 500 articles, conference papers and patents and he has received various prestigious awards for his research. He is also a fellow or member of various professional institutes and societies. He is regularly invited as a keynote speaker at local and international conferences. He has received various teaching and exceptional achiever awards. He is an associate editor of Heat Transfer Engineering and editor of Journal of Porous Media.