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ABSTRACT
Natural convection within a square inclined cavity filled with Al2O3–water nanofluid is investigated numerically. The temperature of the cooled surface is maintained constant, while that of the opposite surface (heating temperature) is varied sinusoidally in time. The remaining walls are considered adiabatic. The parameters governing the problem are the amplitude and the period of the variable temperature, the Rayleigh number, the inclination of the cavity, and the solid volume fraction. A substantial enhancement of heat transfer is obtained by combining the beneficial effects of the variable heating temperature (via its period and amplitude), the inclination of the cavity, and the nanoparticles fraction. In comparison with the constant heating conditions, it is found that both the variable heating temperature and the inclination of the cavity may lead to drastic changes in the flow structure and the corresponding heat transfer. The resonance phenomenon, observed for critical periods of the exciting temperature, is amplified by adding Al2O3 nanoparticles to the base fluid.
Nomenclature
| a | = | amplitude of the periodic temperature, a = a' / |
| cp | = | specific heat, J kg−1 K−1 |
| df | = | equivalent diameter of the base fluid molecule, m |
| ds | = | diameter of the solid nanoparticle, m |
| g | = | acceleration due to the gravity, m s−2 |
| h′ | = | height of the cavity, m |
| H | = | dimensionless heat function |
| ℓ′ | = | length of the cavity, m |
| Nu | = | mean Nusselt number |
| Pr | = | Prandtl number, |
| Ra | = | Rayleigh number, |
| t | = | dimensionless time, t = t′αf/h′2 |
| T | = | dimensionless fluid temperature, |
| T′C | = | temperature of the cooled wall, K |
| Tfr | = | freezing point of the base liquid, K |
| T′H | = | temperature of the heated wall, K |
| = | time-averaged temperature of the heated wall, K | |
| u, v | = | dimensionless horizontal and vertical velocities, (u, v) = (u′h′/αf, v′h′/αf) |
| x, y | = | dimensionless coordinates, (x, y) = (x′/h′, y′/h′) |
Greek symbols
| α | = | thermal diffusivity, m2 s−1 |
| β | = | thermal expansion coefficient, K−1 |
| δt | = | dimensionless time step |
| ϕ | = | nanoparticles volume fraction |
| λ | = | thermal conductivity, W K−1 m−1 |
| μ | = | dynamic viscosity, N s m−2 |
| ν | = | kinematic viscosity, m2 s−1 |
| Ω | = | dimensionless vorticity, Ω = Ω′H′2/αf |
| Ψ | = | dimensionless stream function, Ψ = Ψ′/αf |
| ρ | = | density, kg m−3 |
| θ | = | inclination of the cavity |
| τ | = | dimensionless period of the heating temperature, τ = τ′αf/H′2 |
| τflow | = | dimensionless period of the temporal variation of the Nusselt number |
Subscripts
| C | = | cooled surface |
| cr | = | critical value |
| f | = | fluid |
| H | = | heated surface |
| nf | = | nanofluid |
| max | = | maximum value |
| min | = | minimum value |
| s | = | solid |
Superscript
| ′ | = | dimensional variable |
Additional information
Notes on contributors
Mourad Hati
Mourad Hati is a doctoral student in the Laboratory of Fluid Mechanics and Energetics at the Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco (FSSM). Before, he studied at the Faculty of Sciences and Technics of Errachidia, Moulay Ismail University, Morocco, where he finished his undergraduate studies in 2009. In 2011 he received his master's degree in energetics electronics and automatics, EEA, from FSSM. Currently, he is preparing his national doctorate in heat transfer at the Faculty of Sciences Semlalia in Marrakesh. His thesis focuses on the effect of thermal boundary conditions combined with that of nanofluids on the generated heat transfer in order to identify the optimal conditions leading to improvement of the thermal efficiency of the studied systems.
Abdelghani Raji
Abdelghani Raji is a professor of mechanical engineering at the Faculty of Sciences and Technics of Sultan Moulay Slimane University in Béni-Mellal, Morocco. He received his doctorate degrees from Cadi Ayyad University, Marrakesh, Morocco, in 1994 and 2000. He has published about 70 research papers in international journals and more than 100 papers in conference proceedings. His main range of scientific interests includes heat transfer in fluid and porous media and heat transfer in nanofluids.
Mohammed Hasnaoui
Mohammed Hasnaoui is a professor at Cadi Ayyad University, Faculty of Sciences Semlalia, Marrakesh, Morocco. He received his doctorate degree from the University of Perpignan, France, in 1982 and his Ph.D. in mechanical engineering from Ecole Polytechnique of Montreal, Canada, in 1991. He is the director of the Laboratory of Fluid Mechanincs and Energetics (LMFE); he is a member of the standing committee of JITh and responsible for the Doctoral Formation of Technical Sciences and Engineering. His research activities focus on convective heat transfer in fluid and porous media. He has co-authored more than 300 papers in archival journals and international conferences.
Mohamed Naïmi
Mohamed Naïmi is a professor of mechanical engineering at the Faculty of Sciences and Technics in Béni-Mellal, Morocco. He is the Associate Dean of the Polydisciplinary Faculty in Béni-Mellal. He received his national doctorate (INPL, Nancy, France) and a doctorate of state (Cadi Ayyad University, Marrakesh, Morocco) in 1989 and 2001, respectively. He is a teacher researcher, with the degree of higher teaching professor, at the Faculty of Sciences and Technics of Sultan Moulay Slimane University (Béni-Mellal, Morocco). His research interests include natural, double diffusive, and capillary convections in non-Newtonian fluids. He has published about 70 research papers in international journals.
Mohamed El Abdallaoui
Mohamed El Abdallaoui is a doctoral student in the Physics Department, Faculty of Sciences Semlalia, Cadi Ayyad University, Marrakesh, Morocco. He received the aggregation degree in physical sciences in 1990. He is currently teaching in the preparatory classes for engineering schools in Marrakesh. He obtained his master's degree in 2011 in energetics, electronics and automatics, EEA, at Cadi Ayyad University. In parallel with his teaching work, he is preparing his national doctorate in heat transfer at the Faculty of Sciences Semlalia in Marrakesh. His doctoral research is mainly focused on experimentation with the effectiveness of the lattice Boltzmann method in tackling problems of fluid flow and heat transfer characteristics in complex configurations filled with nanofluids.