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ABSTRACT
Rayleigh–Benard (R-B) convection in water-based alumina (Al2O3) nanofluid is analyzed based on a single-component non-homogeneous volume fraction model (SCNHM) using the lattice Boltzmann method (LBM). The present model accounts for the slip mechanisms such as Brownian and thermophoresis between the nanoparticle and the base fluid. The average Nusselt number at the bottom wall for pure water is compared to the previous numerical data for natural convection in a cavity and a good agreement is obtained. The parameters considered in this study include the Rayleigh number of the nanofluid, the volume fraction of alumina nanoparticle and the aspect ratio of the cavity. For the Al2O3/water nanofluid, it is found that heat transfer rate decreases with an increase of the volume fraction of the nanoparticle. The results are demonstrated and explained with average Nusselt number, isotherms, streamlines, heat lines, and nanoparticle distribution. The effect of nanoparticles on the onset of instability in R-B convection is also analyzed.
Nomenclature
| A | = | aspect ratio |
| Cp | = | specific heat, (J/kgK) |
| DB | = | Brownian diffusion coefficient, (m2/s) |
| DT | = | thermophoretic diffusion coefficient, (m2/s) |
| F | = | force, (N) |
| H | = | height, (m) |
| KB | = | Boltzmann constant, = 1.308 × 10−231/K |
| Le | = | Lewis number, |
| Nu | = | Nusselt number |
| P | = | pressure, (Pa) |
| Pr | = | Prandtl number, |
| Ra | = | Rayleigh number, |
| Re | = | Reynolds number |
| S | = | source term |
| Sc | = | Schmidt number, |
| T | = | temperature, (K) |
| W | = | width, (m) |
| Wi | = | weighing factor |
| d | = | diameter, (nm) |
| ei | = | discrete velocity |
| fi | = | density distribution |
| g | = | acceleration due to gravity, (m/s2) |
| gi | = | temperature distribution |
| hi | = | concentration distribution |
| j | = | flux |
| k | = | thermal conductivity, (W/mK) |
| l | = | mean free path of fluid particles, = 0.17(nm) |
| t | = | time, (s) |
| u | = | horizontal velocity, (m/s) |
| v | = | vertical velocity, (m/s) |
| x&y | = | cartesian coordinates, (m) |
| ρ | = | density, (kg/m3) |
| μ | = | dynamic viscosity, (kg/ms) |
| ν | = | kinematic viscosity, (m2/s) |
| α | = | thermal diffusivity, (m2/s) |
| β | = | thermal expansion coefficient, (1/K) |
| τ | = | lattice relaxation time |
| ϕ | = | nanoparticle volume fraction, (%) |
| Π | = | heat function |
| ∇T | = | temperature gradient, (K/m) |
| ∇ϕ | = | concentration gradient, (% /m) |
| θ | = | non-dimensional temperature |
| ΔT | = | temperature difference, = (Th − Tc)(K) |
| Δt | = | lattice time step |
| Subscripts | = | |
| T | = | temperature |
| avg | = | average |
| bf | = | basefluid |
| c | = | cold |
| conc | = | concentration |
| h | = | hot |
| i | = | discrete lattice direction |
| lbm | = | lattice scale |
| loc | = | local |
| mom | = | momentum |
| nf | = | nanofluid |
| p | = | particle |
| ref | = | reference |
| temp | = | temperature |
| Superscripts | = | |
| eq | = | equilibrium |
| t | = | transpose |
Nomenclature
| A | = | aspect ratio |
| Cp | = | specific heat, (J/kgK) |
| DB | = | Brownian diffusion coefficient, (m2/s) |
| DT | = | thermophoretic diffusion coefficient, (m2/s) |
| F | = | force, (N) |
| H | = | height, (m) |
| KB | = | Boltzmann constant, = 1.308 × 10−231/K |
| Le | = | Lewis number, |
| Nu | = | Nusselt number |
| P | = | pressure, (Pa) |
| Pr | = | Prandtl number, |
| Ra | = | Rayleigh number, |
| Re | = | Reynolds number |
| S | = | source term |
| Sc | = | Schmidt number, |
| T | = | temperature, (K) |
| W | = | width, (m) |
| Wi | = | weighing factor |
| d | = | diameter, (nm) |
| ei | = | discrete velocity |
| fi | = | density distribution |
| g | = | acceleration due to gravity, (m/s2) |
| gi | = | temperature distribution |
| hi | = | concentration distribution |
| j | = | flux |
| k | = | thermal conductivity, (W/mK) |
| l | = | mean free path of fluid particles, = 0.17(nm) |
| t | = | time, (s) |
| u | = | horizontal velocity, (m/s) |
| v | = | vertical velocity, (m/s) |
| x&y | = | cartesian coordinates, (m) |
| ρ | = | density, (kg/m3) |
| μ | = | dynamic viscosity, (kg/ms) |
| ν | = | kinematic viscosity, (m2/s) |
| α | = | thermal diffusivity, (m2/s) |
| β | = | thermal expansion coefficient, (1/K) |
| τ | = | lattice relaxation time |
| ϕ | = | nanoparticle volume fraction, (%) |
| Π | = | heat function |
| ∇T | = | temperature gradient, (K/m) |
| ∇ϕ | = | concentration gradient, (% /m) |
| θ | = | non-dimensional temperature |
| ΔT | = | temperature difference, = (Th − Tc)(K) |
| Δt | = | lattice time step |
| Subscripts | = | |
| T | = | temperature |
| avg | = | average |
| bf | = | basefluid |
| c | = | cold |
| conc | = | concentration |
| h | = | hot |
| i | = | discrete lattice direction |
| lbm | = | lattice scale |
| loc | = | local |
| mom | = | momentum |
| nf | = | nanofluid |
| p | = | particle |
| ref | = | reference |
| temp | = | temperature |
| Superscripts | = | |
| eq | = | equilibrium |
| t | = | transpose |
Acknowledgment
The authors would like to thank P.G. Senapathy Computing Centre, IIT Madras, for providing access to VIRGO SUPER CLUSTER for the simulation. The authors would also like to acknowledge the useful technical discussions and inputs on LBM from Dr. Martin Geier, during his DAAD-IIT faculty exchange stay at IIT Madras.