Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 48, 2005 - Issue 2
170
Views
19
CrossRef citations to date
0
Altmetric
Original Articles

Numerical Study of the Transition Toward Chaos of Two-Dimensional Natural Convection within a Square Cavity

, &
Pages 127-147 | Received 29 Aug 2003, Accepted 24 Jan 2004, Published online: 01 Sep 2006

REFERENCES

  • P. Bergé , Y. Pomeau , and C. Vidal , L'ordre dans le chaos, vers une approche déterministe de la turbulence , Hermann , Paris , 1988 .
  • P. Vadasz , On the Homoclinic Orbit for Convection in a Fluid Layer Heated from Below , Int. J. Heat Mass Transfer , vol. 42 , pp. 3557 – 3561 , 1999 . [CSA]
  • P. Reiterer , C. Lainscsek , F. Schürrer , C. Letellier , and J. Maquet , A Nine-Dimensional Lorenz System to Study High-Dimensional Chaos , J. Phys. A: Math. Gen. , vol. 31 , pp. 7121 – 7139 , 1998 . [CROSSREF]
  • D. R. Moore and N. O. Weiss , Two-Dimensional Rayleigh-Bénard Convection , J. Fluid Mech. , vol. 58 , pp. 289 – 312 , 1973 .
  • A. Skouta , M. A. Randriazanamparany , and M. Daguenet , Etude numérique de la convection naturelle instationnaire bidimensionnelle dans une enceinte allongée, de grand axe horizontal et de section carrée, inclinée eu égard au plan horizontal et chauffée par deux côtés opposés, Int. J. Thermal Sci. , vol. 40, pp. 352–355, 2001. [CSA] [CROSSREF]
  • M. A. Randriazanamparany , Etude numérique des routes vers le chaos par convection naturelle bidimensionnelle dans une enceinte fermée , Doctorate thesis , Université de Perpignan , Perpignan , France , 2001 .
  • D. Mukutmoni and K. T. Yang , Rayleigh-Bénard Convection in a Small Aspect Ratio Enclosure: Part I—Bifurcation to Oscillatory Convection , J. Heat Transfer , vol. 115 , pp. 360 – 366 , 1993 .
  • D. Mukutmoni and K. T. Yang , Rayleigh-Bénard Convection in a Small Aspect Ratio Enclosure: Part II—Bifurcation to Chaos , J. Heat Transfer , vol. 115 , pp. 367 – 376 , 1993 .
  • P. Le Quéré and F. Penot , Numerical and Experimental Investigation of the Transition to Unsteady Natural Convection of Air in a Vertical Differentially Heated Cavity , Proc. ASME Meeting HTD-94 , pp. 75 – 82 , 1987 .
  • R. J. A. Janssen and R. A. W. Henkes , Influence of Prandtl Number on Instability Mechanisms and Transition in a Differentially Heated Square Cavity , J. Fluid Mech. , vol. 47 , pp. 319 – 344 , 1995 .
  • R. A. Kuyper , C. J. Hoogendoorn , and R. A. W. Henkes , Numerical Study of Laminar and Turbulent Natural Convection in an Inclined Enclosure , Int. J. Heat Mass Transfer , vol. 36 , pp. 2899 – 2911 , 1993 . [CROSSREF]
  • E. Saatdjian , Phénomènes de transport et leurs résolutions numériques , Edition Polytechnica , Paris , 1998 .
  • N. N. Yanenko , Méthode à pas fractionnaire , Armand Colin , Paris , 1968 .
  • B. Carnahan , H. A. Luther , and J. O. Wilkes , Applied Numerical Methods , Krieger Publishing Company , 1969 .
  • S. V. Patankar , Numerical Heat Transfer and Fluid Flow , McGraw-Hill , New York , 1980 .
  • B. P. Leonard , A Convectively Stable Third-Order Accurate Finite-Difference Method for Steady Two-Dimensional Flow and Heat Transfer , pp. 211 – 226 , Hemisphere Publishing Corporation , Washington , DC , 1983 .
  • B. P. Leonard , A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation , Comput. Meth. Appl. Mech. Eng. , vol. 19 , pp. 59 – 98 , 1979 . [CSA] [CROSSREF]
  • B. P. Leonard , Elliptic Systems: Finite-Difference Method IV , in Handbook of Numerical Heat Transfer , pp. 347 – 378 , Wiley , New York , 1988 .
  • R. C. Hilborn , Chaos and Nonlinear Dynamics—An Introduction for Scientists and Engineers , Oxford University Press , 1994 .
  • E. Ott , Chaos in Dynamical Systems , Cambridge University Press , Cambridge , 1993 .

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.