Diffusion induced chaos in a closed loop thermosyphon

SIAM Journal on Applied Mathematics

Volumn 58, Issue 4, 1998, Pages 1072-1093

  Rodríguez Bernal, Aníbal ^a   Van Vleck, Erik S ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b Department of Metallurgical and Materials Engineering   (United States)

Author keywords

Asymptotic behavior; Inertial manifold; Natural convection

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); DIFFUSION; HEAT FLUX; MATHEMATICAL MODELS; NATURAL CONVECTION; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SIPHONS;

CLOSED LOOP THERMOSYPHON; INERTIAL MANIFOLD; LORENZ EQUATION;

CHAOS THEORY;

EID: 0032141002     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139996304184     Document Type: Article

References (20)

1. A. M. BLOCH AND E. S. TITI, On the dynamics of rotating elastic beams, in New Trends in System Theory, Progr. Systems Control Theory 7, Birkhäuser Boston, Boston, MA, 1991, pp. 128-135.
2. K. CHEN, On the oscillatory instability of closed-loop thermosyphons, J. Heat Transfer, 107 (1985), pp. 826-832.
3. J. H. CURRY, A generalized Lorenz system, Comm. Math. Phys., 60 (1978), pp. 193-204.
4. C. FOIAS, G. SELL, AND R. TEMAM, Inertial manifolds for nonlinear evolutionary equations, J. Differential Equations, 73 (1988), pp. 309-353.
5. R. GREIF, Y. ZVIRIN, AND A. MERTOL, The transient and stability behavior of a natural convection loop, J. Heat Transfer, 101 (1979), pp. 684-688.
6. J. K. HALE, Asymptotic Behavior of Dissipative Systems, AMS, Providence, RI, 1988.
7. J. E. HART, Observations of complex oscillations in a closed thermosyphon, J. Heat Transfer, 107 (1985), pp. 833-839.
8. D. HENRY, Geometric theory of semilinear parabolic equations, Lecture Notes in Math. 840, Springer-Verlag, Berlin, New York, 1982.
9. M. A. HERRERO AND J. J. L. VELAZQUEZ, Stability analysis of a closed thermosyphon, European J. Appl. Math., 1 (1990), pp. 1-24.
10. D. JAPIKSE, Advances in thermosyphon technology, Adv. Heat Transfer, 9 (1973), pp. 1-111.
11. J. B. KELLER, Periodic oscillations in a model of thermal convections, J. Fluid Mech., 26 (1966), pp. 599-606.
12. A. LIN̄ÁN, Analytical description of chaotic oscillations in a toroidal thermosyphon, in Fluid Physics, Lecture Notes of Summer Schools, M. G. Velarde and C. I. Christov, eds., World Scientific, River Edge, NJ, 1994, pp. 507-523.
13. E. N. LORENZ, Deterministic nonperiodic flow, J. Atmospheric Sci., 20 (1963), pp. 130-141.
14. A. RODRÍGUEZ-BERNAL, Attractors and inertial manifolds for the dynamics of a closed thermosyphon, J. Math. Anal. Appl., 193 (1995), pp. 942-965.
15. A. RODRÍGUEZ-BERNAL, Inertial manifold for dissipative semiflows in Banach spaces, Appl. Anal., 37 (1990), pp. 95-141.
16. A. RODRÍGUEZ-BERNAL AND E. S. VAN VLECK, Complex oscillations in a closed thermosyphon, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8 (1998).
17. C. SPARROW, The Lorenz Equations: Bifurcation, Chaos, and Strange Attractors, Springer-Verlag, Berlin, New York, 1982.
18. A. M. STUART, Perturbation theory for infinite-dimensional dynamical systems, in Theory and Numerics of Ordinary and Partial Differential Equations, M. Ainsworth, J. Levesley, W. A. Light, and M. Marietta, eds., Oxford University Press, Oxford, UK, 1994.
19. J. J. L. VELÁZQUEZ, On the dynamics of a closed thermosyphon, SIAM J. Appl. Math., 54 (1994), pp. 1561-1593.
20. P. WELANDER, On the oscillatory instability of a differentially heated fluid loop, J. Fluid Mech., 29 (1967), pp. 17-30.