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Abstract
This paper analyzes heat transfer and fluid flow of natural convection in inclined cavity filled with CuO–water nanofluid and differentially heated. Conservation of mass, momentum, and energy equations are solved numerically by a control volume finite-element method using the SIMPLER algorithm for pressure–velocity coupling. The Prandtl number is fixed at 7.02, corresponding to water. Aspect ratio and solid volume fraction are varied from 0.5 to 4 and from 0% to 4%, respectively. The inclination angle is varied from 0° to 90° and used as a control parameter to investigate flow mode-transition and the accompanying hysteresis phenomenon (multi-steady solutions). It is found that the efficiency of heat transfer is improved by the addition of nanoparticles into base fluid; however, there is an optimum solid volume fraction that maximizes the heat transfer rate. Numerical results show also that the diameter of solid particle is an important parameter that affects the heat transfer efficiency; its impact is more important than the concentration itself. Effects of inclination angle on streamlines and on thermal boundary layer are presented. Combined effects of aspect ratio and inclination angle on heat transfer and hysteresis region are analyzed.
NOMENCLATURE
| Ar | = | aspect ratio of the cavity (L/H) |
| Cp | = | specific heat at constant pressure (J kg−1 K−1) |
| ds | = | nanoparticle diameter (m) |
| g | = | gravitational acceleration (m s−2) |
| H | = | height of the cavity (m) |
| k | = | thermal conductivity (W m−1 K−1) |
| L | = | length of the cavity (m) |
| Nu(x) | = | local Nusselt number ( |
| Nu | = | space averaged Nusselt number |
| p | = | pressure (nondimensionalized by ρnfαf/H2) |
| Pr | = | Prandtl number (νf /αf) |
| Ra | = | Rayleigh number (gβfH3(Th – Tc)/νfαf) |
| T | = | temperature (K) |
| u,v | = | dimensionless velocity components (normalized by αf /H) |
| x,y | = | dimensionless coordinates (normalized by H) |
Greek Symbols
| α | = | thermal diffusivity (k/ρCp)(m2 s−1) |
| β | = | thermal expansion coefficient (K−1) |
| φ | = | solid volume fraction |
| θ | = | dimensionless temperature(T – Tc)/(Th – Tc) |
| μ | = | dynamic viscosity of the fluid (kg m−1 s−1) |
| ν | = | kinematic viscosity of the fluid (μ /ρ) (m2 s−1) |
| ρ | = | density of the fluid (kg m−3) |
| ω | = | inclination angle of the cavity |
Subscripts
| c | = | cold |
| eff | = | effective |
| h | = | hot |
| f | = | fluid |
| nf | = | CuO–water nanofluid |
| s | = | solid |
Additional information
Notes on contributors
Mefteh Bouhalleb
Mefteh Bouhalleb is a Ph.D. student at the unit of Computational Fluid Dynamics and Transfer Phenomena in the Department of Mechanics at the National Engineering School of Sfax, Tunisia under the supervision of Prof. Hassen Abbassi. He is currently working on heat transfer enhancement by nanofluids.
Hassen Abbassi
Hassen Abbassi is a professor of physics at the University of Sfax, Tunisia. He obtained his Ph.D. in physics in 2001 from the Sciences Faculty of Tunis and obtained his Habilitation in 2004 from the University of Sfax. Currently, he directs a research group in the fields of fluid flow and heat transfer at the National Engineering School of Sfax, Tunisia. His research interests include heat exchangers, heat transfer in nanofluids, flows around obstacles, porous media, magnetohydrodynamics, and computational fluid dynamics. He has published about 35 research papers in international journals and conferences and a textbook at the Tunisian national center of publication.