Diffusion induced chaos in a closed loop thermosyphon
| dc.contributor.author | Rodríguez Bernal, Aníbal | |
| dc.contributor.author | Van Vleck, Erik S. | |
| dc.date.accessioned | 2023-06-20T17:08:41Z | |
| dc.date.available | 2023-06-20T17:08:41Z | |
| dc.date.issued | 1998-08 | |
| dc.description.abstract | The dynamics of a closed loop thermosyphon are considered. The model assumes a prescribed heat flux along the loop wall and the contribution of axial diffusion. The well-posedness of the model which consists of a coupled ODE and PDE is shown for both the case with diffusion and without diffusion. Boundedness of solutions, the existence of an attractor, and an inertial manifold is proven, and an exact reduction to a low-dimensional model is obtained for the diffusion case. The reduced systems may have far fewer degrees of freedom than the reduction to the inertial manifold. For the three mode models, equivalence with the classical Lorenz equations is shown. Numerical results are presented for five mode models. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | NATO | |
| dc.description.sponsorship | CICYT (Spain) | |
| dc.description.sponsorship | EEC | |
| dc.description.sponsorship | NSF | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17894 | |
| dc.identifier.doi | 10.1137/S0036139996304184 | |
| dc.identifier.issn | 0036-1399 | |
| dc.identifier.officialurl | http://www.jstor.org/stable/10.2307/118320 | |
| dc.identifier.relatedurl | http://www.jstor.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57838 | |
| dc.issue.number | 4 | |
| dc.journal.title | SIAM Journal on applied mathematics | |
| dc.language.iso | eng | |
| dc.page.final | 1093 | |
| dc.page.initial | 1072 | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.relation.projectID | CRG-940655 | |
| dc.relation.projectID | PB93-0438 | |
| dc.relation.projectID | SC1-CT91-0732 | |
| dc.relation.projectID | DMS-9505049 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.986 | |
| dc.subject.keyword | Natural convection | |
| dc.subject.keyword | Asymptotic behavior | |
| dc.subject.keyword | Inertial manifold | |
| dc.subject.keyword | Three mode models | |
| dc.subject.keyword | Five mode models | |
| dc.subject.keyword | Thermosiphon | |
| dc.subject.keyword | Dynamics | |
| dc.subject.ucm | Funciones (Matemáticas) | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | Diffusion induced chaos in a closed loop thermosyphon | |
| dc.type | journal article | |
| dc.volume.number | 58 | |
| dcterms.references | 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. K. Chen, On the oscillatory instability of closed-loop thermosyphons, J. Heat Transfer, 107 (1985), pp. 826–832. J. H. Curry, A generalized Lorenz system, Comm. Math. Phys., 60 (1978), pp. 193–204. C. Foias, G. Sell, and R. Temam, Inertial manifolds for nonlinear evolutionary equations, J. Differential Equations, 73 (1988), pp. 309–353. R. Greif, Y. Zvirin, and A. Mertol, The transient and stability behavior of a natural con- vection loop, J. Heat Transfer, 101 (1979), pp. 684–688. J. K. Hale, Asymptotic Behavior of Dissipative Systems, AMS, Providence, RI, 1988. J. E. Hart, Observations of complex oscillations in a closed thermosyphon, J. Heat Transfer, 107 (1985), pp. 833–839. D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Math. 840, Springer-Verlag, Berlin, New York, 1982. M. A. Herrero and J. J. L. Velázquez, Stability analysis of a closed thermosyphon, European J. Appl. Math., 1 (1990), pp. 1–24. D. Japikse, Advances in thermosyphon technology, Adv. Heat Transfer, 9 (1973), pp. 1–111. J. B. Keller, Periodic oscillations in a model of thermal convections, J. Fluid Mech., 26 (1966), pp. 599–606. A. Liñán, 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. E. N. Lorenz, Deterministic nonperiodic flow, J. Atmospheric Sci., 20 (1963), pp. 130–141. A. Rodríguez-Bernal, Attractors and inertial manifolds for the dynamics of a closed ther- mosyphon, J. Math. Anal. Appl., 193 (1995), pp. 942–965. A. Rodríguez-Bernal, Inertial manifold for dissipative semiflows in Banach spaces, Appl. Anal., 37 (1990), pp. 95–141. A. Rodríguez-Bernal and E. S. Van Vleck, Complex oscillations in a closed thermosyphon, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 8 (1998). C. Sparrow, The Lorenz Equations: Bifurcation, Chaos, and Strange Attractors, Springer- Verlag, Berlin, New York, 1982. 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. Marletta, eds., Oxford University Press, Oxford, UK, 1994. J. J. L. Velázquez, On the dynamics of a closed thermosyphon, SIAM J. Appl. Math., 54 (1994), pp. 1561–1593. P. Welander, On the oscillatory instability of a differentially heated fluid loop, J. Fluid Mech., 29 (1967), pp. 17–30. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 | |
| relation.isAuthorOfPublication.latestForDiscovery | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 |
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