Stabilizing interplay between thermodiffusion and viscoelasticity in a closed-loop thermosyphon

Justine  Yasappan; Ángela  Jiménez-Casas; Mario  Castro

doi:10.3934/dcdsb.2015.20.3267

Article Contents

2015, Volume 20, Issue 9: 3267-3299. Doi: 10.3934/dcdsb.2015.20.3267

This issue Previous Article Global asymptotical stability of the coexistence fixed point of a Ricker-type competitive model Next Article

Stabilizing interplay between thermodiffusion and viscoelasticity in a closed-loop thermosyphon

1.
Grupo de Dinámica No Lineal (DNL), Escuela Técnica Superior de Ingeniería (ICAI), Universidad Pontificia Comillas, Madrid E-28015

Received: May 31, 2013

Revised: April 30, 2014

Published: October 2015

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Abstract

Viscoelastic fluids represent a major challenge both from an engineering and from a mathematical point of view. Recently, we have shown that viscoelasticity induces chaos in closed-loop thermosyphons. This induced behavior might interfere with the engineering choice of using a specific fluid. In this work we show that the addition of a solute to the fluid can, under some conditions, stabilize the system due to thermodiffusion (also known as the Soret effect). Unexpectedly, the role of viscoelasticity is opposite to the case of single-element fluids, where it (generically) induces chaos. Our results are derived by combining analytical results based on the projection of the dynamics on an inertial manifold as well as numerical simulations characterized by the calculation of Lyapunov exponents.

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Mathematics Subject Classification: Primary: 34D45, 35B40, 35K, 35Q, 58F; Secondary: 74D05.

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