# American Institute of Mathematical Sciences

2013, 2013(special): 375-384. doi: 10.3934/proc.2013.2013.375

## Finite-dimensional behavior in a thermosyphon with a viscoelastic fluid

 1 Grupo Dinámica No Lineal(ICAI), Universidad Pontificia Comillas, C/Alberto Aguilera 23, 28015 Madrid 2 Grupo Interdisciplinar de Sistemas Complejos (GISC) and Grupo de Dinmica No Lineal (DNL), Escuela Tcnica Superior de Ingeniera (ICAI), Universidad Pontificia Comillas, E28015, Madrid, Spain 3 Grupo de Dinmica No Lineal (DNL), Departamento de Matemtica Aplicada y Computacin, Escuela Tcnica Superior de Ingeniera (ICAI), Universidad Ponti cia Comillas, E28015, Madrid, Spain

Received  July 2012 Published  November 2013

We analyse the motion of a viscoelastic fluid in the interior of a closed loop thermosyphon under the effects of natural convection. We consider a viscoelastic fluid described by the Maxwell constitutive equation. This fluid presents elastic-like behavior and memory effects. We study the asymptotic properties of the fluid inside the thermosyphon and derive the exact equations of motion in the inertial manifold that characterize the asymptotic behavior. Our work is a generalization of some previous results on standard (Newtonian) fluids.
Citation: A. Jiménez-Casas, Mario Castro, Justine Yassapan. Finite-dimensional behavior in a thermosyphon with a viscoelastic fluid. Conference Publications, 2013, 2013 (special) : 375-384. doi: 10.3934/proc.2013.2013.375
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##### References:
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