http://orcid.org/0000-0003-3582-300X
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ABSTRACT
This paper analyzes heat transfer and fluid flow of natural convection in an inclined square enclosure filled with different types of nanofluids having various shapes of nanoparticles in the presence of oriented magnetic field. The Galerkin weighted residual finite element method has been employed to solve the governing non-dimensional partial differential equations. In the numerical simulations, water, ethylene glycol, and engine oil containing copper, alumina, titanium dioxide nanoparticles are considered. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, magnetic field inclination angle, geometry inclination angle on the fluid flow and heat transfer are investigated. The results indicate that increment of the Rayleigh number and nanoparticle volume fraction increase the heat transfer rate in a significant way, whereas, increment of the Hartmann number decreases the overall heat transfer rate. It is also observed that a blade shape nanoparticle gives higher heat transfer rate compared to other shapes of nanoparticles. The critical geometry inclination angle at which the maximum heat transfer rate is achieved depends on the nanoparticle volume fraction as well as on the magnetic field orientation. These results are new and have direct applications in solar thermal collectors and thermal insulator of buildings.
| Nomenclature | ||
| B0 | = | magnetic field strength [N·m−1·A−1] |
| cp | = | specific heat [J.kg−1.K−1] |
| g | = | gravitational acceleration [m.s−2] |
| Ha | = | Hartmann number, dimensionless |
| k | = | thermal conductivity [W.m−1.K−1] |
| L | = | enclosure length [m] |
| Nu | = | Nusselt number, dimensionless |
| n | = | empirical shape factor |
| p | = | fluid pressure [Pa] |
| P | = | fluid pressure, dimensionless |
| Pr | = | Prandtl number, dimensionless |
| Ra | = | Rayleigh number, dimensionless |
| Sr | = | Shear rate [s− 1] |
| T | = | temperature [K] |
| u,v | = | velocity components in x,y directions [m.s−1] |
| U, V | = | dimensionless velocity components |
| = | average velocity magnitude [m.s−1] | |
| x, y | = | Cartesian coordinates [m] |
| X, Y | = | dimensionless coordinates |
| Greek Symbols | ||
| α | = | thermal diffusivity [m−2/s] |
| β | = | thermal expansion coefficient [1/K] |
| γ | = | magnetic field orientation angle [rad] |
| δ | = | geometry (cavity) inclination angle [rad] |
| θ | = | dimensionless temperature |
| φ | = | solid volume fraction |
| ψ | = | sphericity |
| μ | = | dynamic viscosity [N.s.m−2] |
| = | kinematic viscosity [m2.s−1] | |
| ρ | = | density [kg.m−3] |
| σ | = | electrical conductivity [S.m−1] |
| Subscripts | ||
| av | = | average |
| C | = | cold wall |
| c | = | critical |
| f | = | base fluid |
| Hs | = | hot wall |
| nf | = | nanofluid |
| s | = | solid particle |
Additional information
Funding
Notes on contributors
Khamis S. Al Kalbani
Khamis S. Al Kalbani is a Ph.D. student in the Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, Sultanate of Oman under the supervision of Dr. M. M. Rahman. He received his M. Sc. degree in Applied Mathematics in 2008 from Sultan Qaboos University. Currently, he is working on mathematical modeling of nanofluid.
Mohammad M. Rahman
Mohammad M. Rahman is an Associate Professor of Applied Mathematics at the Sultan Qaboos University, Sultanate of Oman. He received his M.Sc. degree in 1994 from the University of Dhaka, and Ph.D. in 2003 in Applied Mathematics from the University of Glasgow, U.K. His research interests include mathematical fluid mechanics, nano-fluidic phenomena, magnetohydrodynamics, heat and mass transfer, transport in porous media, and bio-fluid flows. He has supervised 15 Ph.D./M.Sc. students. Currently, he is involved in supervising several Ph.D. and M.Sc. students. He has published more than 100 research papers. He is an active member of several scholarly societies.
Shariful Alam
Md. Shariful Alam is a Professor in the Department of Mathematics, Jagannath University, Dhaka, Bangladesh. He received his Ph. D. degree in Applied Mathematics from the University of Dhaka in 2009 under the prudent supervision of Dr. M. M. Rahman. His research interests include computational fluid dynamics and nano-fluidic phenomena. He has published more than 50 research papers in international journals. Currently, he is working as a post-doctoral research fellow in the Department of Mathematics and Statistics, Sultan Qaboos University, Sultanate of Oman.
Nasser Al-Salti
Nasser Al-Salti is an Assistant Professor of Applied Mathematics in the Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, Sultanate of Oman. He received his Ph. D. degree in Applied Mathematics in 2010 from the University of St Andrews, United Kingdom. His research interests include MHD and magnetic reconnection, nano-fluidic phenomenon, fractional differential equations. Currently, he is the Assistant Dean for Training and Community Services in the College of Science, Sultan Qaboos University.
Ibrahim A. Eltayeb
Ibrahim A. Eltayeb is a Professor of Applied Mathematics at the Sultan Qaboos University, Sultanate of Oman. He received his Ph.D. degree in Applied Mathematics in 1972 from the University of Newcastle-upon-Tyne, United Kingdom. His research interests concern the applications of differential equations to mathematical models of geophysical, industrial and environmental problems. He is a Fellow of the African Academy of Sciences, Honorary Fellow of the Royal Astronomical Society of London, Fellow of TWAS and Corresponding Fellow of the Royal Society of Edinburg. He has received several international awards.