- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Submit a Manuscript
- Subscription Information
- Table of Contents
Volume 2012 (2012), Article ID 614712, 10 pages
Rayleigh-Bénard Convection of Non-Newtonian Power-Law Fluids with Temperature-Dependent Viscosity
1Laboratory of Flows and Transfers Modelling (LAMET), Physics Department, Faculty of Sciences and Technologies, Sultan Moulay Slimane University, BP 523, Beni-Mellal, Morocco
2Laboratory of Fluid Mechanics and Energetics (LMFE), Physics Department, Faculty of Sciences Semlalia, Cadi Ayyad University, BP 2390, Marrakech, Morocco
Received 30 September 2012; Accepted 16 October 2012
Academic Editors: G. L. Aranovich, P. Espeau, and H. Hirao
Copyright © 2012 Mourad Kaddiri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- B. Gebhart, Y. Jaluria, R. L. Mahajan, and B. Sammakia, Buoyancy-Induced Flows and Transport, Hemisphere, Washington, DC, USA, 1985.
- S. W. Churchill, Heat Exchanger Design Handbook, section 2.5.8., Hemisphere Publishing Corporation, New York, NY, USA, 1983.
- A. Bejan, Convection Heat Transfer, John Wiley Sons, New York, NY, USA, 1984.
- H. Ozoe and S. W. Churchill, “Hydrodynamic stability and natural convection in Ostwald-De Waele and Ellis fluids: the development of a numerical solution,” American Institute of Chemical Engineers Journal, vol. 18, pp. 1196–1207, 1972.
- H. M. Park and D. H. Ryu, “Rayleigh-Bérnard convection of viscoelastic fluids in finited domains,” Journal of Non-Newtonian Fluid Mechanics, vol. 98, no. 2-3, pp. 169–184, 2001.
- M. Ohta, M. Ohta, M. Akiyoshi, and E. Obata, “A numerical study on natural convective heat transfer of pseudoplastic fluids in a square cavity,” Numerical Heat Transfer A, vol. 41, no. 4, pp. 357–372, 2002.
- H. Inaba, C. Dai, and A. Horibe, “Natural convection heat transfer of microemulsion phase-change-material slurry in rectangular cavities heated from below and cooled from above,” International Journal of Heat and Mass Transfer, vol. 46, no. 23, pp. 4427–4438, 2003.
- M. Lamsaadi, M. Naïmi, and M. Hasnaoui, “Natural convection of non-Newtonian power law fluids in a shallow horizontal rectangular cavity uniformly heated from below,” Heat and Mass Transfer, vol. 41, no. 3, pp. 239–249, 2005.
- J. Zhang, D. Vola, and I. A. Frigaard, “Yield stress effects on Rayleigh-Bénard convection,” Journal of Fluid Mechanics, vol. 566, pp. 389–419, 2006.
- N. J. Balmforth and A. C. Rust, “Weakly nonlinear viscoplastic convection,” Journal of Non-Newtonian Fluid Mechanics, vol. 158, no. 1–3, pp. 36–45, 2009.
- A. Vikhansky, “Thermal convection of a viscoplastic liquid with high Rayleigh and Bingham numbers,” Physics of Fluids, vol. 21, no. 10, Article ID 103103, 2009.
- D. D. Gray and A. Giorgini, “The validity of the boussinesq approximation for liquids and gases,” International Journal of Heat and Mass Transfer, vol. 19, no. 5, pp. 545–551, 1976.
- D. A. Yuen, W. R. Peltier, and G. Schubert, “On the existence of a second scale of convection in the upper mantle,” Geophysical Journal, Royal Astronomical Society, vol. 65, no. 1, pp. 171–190, 1981.
- V. Scirocco, R. Devienne, and M. Lebouché, “Ecoulement laminaire et transfert de chaleur pour un fluide pseudo-plastique dans la zone d'entrée d'un tube,” International Journal of Heat and Mass Transfer, vol. 28, no. 1, pp. 91–99, 1985.
- S. Shin and Y. I. Cho, “Laminar heat transfer in a rectangular duct with a non-Newtonian fluid with temperature-dependent viscosity,” International Journal of Heat and Mass Transfer, vol. 37, no. 1, pp. 19–30, 1994.
- K. C. Stengel, D. S. Oliver, and J. R. Booker, “Onset of convection in a variable-viscosity fluid,” Journal of Fluid Mechanics, vol. 120, pp. 411–431, 1982.
- F. M. Richter, H. C. Nataf, and S. Daly, “Heat transfer and horizontally averaged temperature of convection with large viscosity variations,” Fluid Mechanics, vol. 129, pp. 173–192, 1983.
- F. H. Busse and H. Frick, “Square-pattern convection in fluids with strongly temperature-dependent viscosity,” Journal of Fluid Mechanics, vol. 150, pp. 451–465, 1985.
- D. B. White, “The plan forms and onset of convection with a temperature-dependent viscosity,” Journal of Fluid Mechanics, vol. 191, pp. 247–286, 1988.
- A. Bottaro, P. Metzener, and M. Matalon, “Onset and two-dimensional patterns of convection with strongly temperature-dependent viscosity,” Physics of Fluids A, vol. 4, no. 4, pp. 655–663, 1992.
- A. Davaille and C. Jaupart, “Onset of thermal convection in fluids with temperature-dependent viscosity: application to the oceanic mantle,” Journal of Geophysical Research, vol. 99, no. 10, pp. 19–866, 1994.
- S. E. Zaranek and E. M. Parmentier, “The onset of convection in fluids with strongly temperature-dependent viscosity cooled from above with implications for planetary lithospheres,” Earth and Planetary Science Letters, vol. 224, no. 3-4, pp. 371–386, 2004.
- M. C. Kim and C. K. Choi, “The onset of buoyancy-driven convection in fluid layers with temperature-dependent viscosity,” Physics of the Earth and Planetary Interiors, vol. 155, no. 1-2, pp. 42–47, 2006.
- V. S. Solomatov and A. C. Barr, “Onset of convection in fluids with strongly temperature-dependent, power-law viscosity,” Physics of the Earth and Planetary Interiors, vol. 155, no. 1-2, pp. 140–145, 2006.
- V. S. Solomatov and A. C. Barr, “Onset of convection in fluids with strongly temperature-dependent, power-law viscosity. 2. Dependence on the initial perturbation,” Physics of the Earth and Planetary Interiors, vol. 165, no. 1-2, pp. 1–13, 2007.
- N. J. Balmforth and A. Provenzale, Geophysical Aspects of Non-Newtonian Fluid Mechanics, vol. 582 of Liberal National Party, Springer, 2001.
- P. J. Roache, Computational Fluid Dynamics, Hermosa Publishers, Albuquerque, NM, USA, 1982.
- C. Métivier and C. Nouar, “Linear stability of the Rayleigh-Bénard Poiseuille flow for thermodependent viscoplastic fluids,” Journal of Non-Newtonian Fluid Mechanics, vol. 163, no. 1–3, pp. 1–8, 2009.
- S. Kimura and A. Bejan, “The heatline visualization of convective heat transfer,” ASME Journal of Heat Transfer, vol. 105, pp. 916–919, 1983.
- N. Ouertatani, N. Ben Cheikh, B. Ben Beya, and T. Lili, “Numerical simulation of two-dimensional Rayleigh-Bénard convection in an enclosure,” Comptes Rendus, vol. 336, no. 5, pp. 464–470, 2008.
- Y. I. Cho and J. P. Harnett, “Non-newtonian fluids in circular pipe flow,” Advances in Heat Transfer, vol. 15, pp. 59–141, 1982.