Publication Cover
Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 63, 2013 - Issue 5
88
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

A Quasi-Implicit Time-Advancing Scheme for 3-D Rayleigh-Bénard Convection

, &
Pages 371-394 | Received 13 Sep 2012, Accepted 08 Nov 2012, Published online: 28 Apr 2013

REFERENCES

  • F. B. Lipps , Numerical Simulation of Three–Dimensional Bénard Convection in Air , J. Fluid Mech. , vol. 75 , pp. 113 – 148 , 1976 .
  • T. Inagaki , M. Hatori , T. Suzuki , and Y. Shina , Heat Transfer and Fluid Flow of Bénard–Cell Convection in Rectangular Container with Free Surface Sensed by Infrared Thermography , J. Visualization , vol. 9 , pp. 145 – 160 , 2006 .
  • K. Krishan , H. Kurtuldu , M. F. Schatz , M. Gameiro , K. Mischaikow , and S. Madruga , Homology and Symmetry Breaking in Rayleigh-Bénard Convection: Experiments and Simulations , Phys. Fluids , vol. 19 , 117105 , 2007 .
  • J. Prat , J. M. Massaguer , and I. Mercader , Large-Scale Flows and Resonances in 2-D Thermal Convection , Phys. Fluids , vol. 7 , pp. 121 – 134 , 1995 .
  • E. Zienicke , N. Seehafer , and F. Feudel , Bifurcations in Two-Dimensional Rayleigh–Bénard Convection , Phys. Rev. E , vol. 57 , pp. 428 – 435 , 1998 .
  • F. Stella and E. Bucchignani , Rayleigh–Bénard Convection in Limited Domains: Part 1—Oscillatory Flow , Numer. Heat Transfer A , vol. 36 , pp. 1 – 16 , 1999 .
  • E. Bucchignani and F. Stella , Rayleigh–Bénard Convection in Limited Domains: Part 2—Transition to Chaos , Numer. Heat Transfer A , vol. 36 , pp. 17 – 34 , 1999 .
  • P. Y. Tzeng and M. H. Liu , Direct-Simulation Monte Carlo Modeling on Two-Dimensional Rayleigh–Bénard Instabilities of Rarefied Gas , Numer. Heat Transfer A , vol. 47 , pp. 805 – 823 , 2005 .
  • S. Nasuno , M. Sano , and Y. Sawada , Saptial Instabilities and Onset of Chaos in Rayleigh–Bénard System with Intermediate Aspect Ratio , J. Phys. Soc. Japan , vol. 57 , pp. 3357 – 3364 , 1988 .
  • F. H. Busse and R. M. Clever , Instabilities of Convection Rolls in a Fluid of Moderate Prandtl Number , J. Fluid Mech. , vol. 91 , pp. 319 – 335 , 1979 .
  • F. H. Busse , Transition to Turbulence in Rayleigh–Bénard Convection , in H. L. Swinney and J. P. Gollub (eds.), Topics in Applied Physics , vol. 45 , pp. 87 – 137 , Springer-Verlag , Berlin , 1981 .
  • R. Krishnamurti , On the Transition to Turbulent Convection, Part 1: The Transition from Two to Three Dimensional Flow , J. Fluid Mech. , vol. 42 , pp. 295 – 307 , 1970 .
  • R. Kessler , Nonlinear Transition in Three–Dimensional Convection , J. Fluid Mech. , vol. 174 , pp. 357 – 379 , 1987 .
  • G. Ahlers and R. P. Behringer , Evolution of Turbulence from Rayleigh–Bénard Instability , Phys. Rev. Lett. , vol. 40 , pp. 712 – 716 , 1978 .
  • D. Mukutmoni and K. T. Yang , Pattern Selection for Rayleigh–Bénard Convection in Intermediate Aspect Ratio Boxes , Numer. Heat Transfer A , vol. 27 , pp. 621 – 637 , 1995 .
  • P. Kolodner , R. W. Walden , A. Passner , and C. M. Surko , Rayleigh–Bénard Convection in An Intermediate-Aspect-Ratio Rectangular Container , J. Fluid Mech. , vol. 163 , pp. 195 – 226 , 1986 .
  • Y. J. Jan , and W. H. Sheu , A Quasi-Implicit Time Advancing Scheme for Unsteady Incompressible Flow, Part I: Validation , Comput. Meth. Appl. Mech. Eng. , vol. 196 , pp. 4755 – 4770 , 2007 .
  • C. M. Rhie and W. L. Chow , Numerical Study of the Turbulent Flow Past an Airfoil with Trailing Edge Separation , AIAA J. , vol. 21 , pp. 1525 – 1532 , 1983 .
  • R. J. Krane and J. Jessee , Some Detailed Field Measurements for a Natural Convection Flow in a Vertical Square Enclosure , Proc. 1st ASME-JSME Thermal Engineering Joint Conf. , vol. 1 , pp. 323 – 329 , 1983 .
  • G. Barakos and E. Mitsoulis , Natural Convection Flow in a Square Cavity Revisited Laminar and Turbulent Models with Wall Functions , Int. J. Numer. Meth. Fluids , vol. 18 , pp. 695 – 719 , 1994 .
  • K. G. T. Hollands , S. E. Unny , G. D. Raithby , and L. Konicek , Free Convection Heat Transfer across Inclined Air Layers, J. Heat Transfer , vol. 98, pp. 189–193, 1976.
  • B. Gebhart , Y. Jaluria , R. L. Mahajan , and B. Sammakia , Buoyancy-Induced Flows and Transport , Hemisphere , New York , 1988 .
  • S. Casado , W. González-Viñas , and H. Mancini , Testing the Kibble–Zurek Mechanism in Rayleigh–Bénard Convection , Phys. Rev. E , vol. 74 , 047101 , 2006 .
  • S. Casado , W. González-Viñas , S. Boccaletti , P. L. Ramazza , and H. Mancini , The Birth of Defects in Pattern Formation: Testing of the Kibble–Zurek Mechanism , Eur. Phys. J. Special Topics , vol. 146 , pp. 87 – 98 , 2007 .
  • D. Mishra , K. Muralidhar , and P. Munshi , Experimental Study of Rayleigh–Benard Convection at Intermediate Rayleigh Numbers Using Interferometric Tomography , Fluid Dynam. Res. , vol. 25 , pp. 231 – 255 , 1998 .
  • S. V. Patankar , Numerical Heat Transfer and Fluid Flow , Hemisphere , New York , 1980 .
  • O. Rahli , R. Bennacer , K. Bouhadef , and D. E. Ameziani , Three-Dimensional Mixed Convection Heat and Mass Transfer in a Rectangular Duct: Case of Longitudinal Rolls , Numer. Heat Transfer B , vol. 59 , pp. 349 – 371 , 2011 .
  • K. Zhang , M. Yang , and Y. Zhang , A Compact Finite-Difference Scheme Based on the Projection Method for Natural-Convection Heat Transfer , Numer. Heat Transfer B , vol. 61 , pp. 259 – 278 , 2012 .
  • X. Nicolas , M. Medale , S. Glockner , and S. Gounand , Benchmark Solution for a Three-Dimensional Mixed-Convection Flow, Part 1: Reference Solutions , Numer. Heat Transfer B , vol. 61 , pp. 325 – 345 , 2012 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.