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Diffusion Induced Chaos in a Closed Loop Thermosyphon
Rodriguez-Bernal, Anibal Van Vleck, Erik S.
Rodriguez-Bernal, Anibal
Van Vleck, Erik S.
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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.
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This is the published version, also available here: http://dx.doi.org/10.1137/S0036139996304184.
Date
1998-08-05
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Society for Industrial and Applied Mathematics
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Keywords
natural convection, asymptotic behavior, inertial manifold
Citation
Rodriguez-Bernal, Anibal & Van Vleck, Erik. "Diffusion Induced Chaos in a Closed Loop Thermosyphon." (1998) SIAM J. Appl. Math., 58(4), 1072–1093. (22 pages). http://dx.doi.org/10.1137/S0036139996304184.