Asymptotic behaviour of a closed‐loop thermosyphon with linear friction and viscoelastic binary fluid

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 even when we consider binary fluids, this is, when we consider a solute in the fluid, as water and antifreezes, for example. In this work, we consider a linear friction law, and we show that in this case with the addition of a solute to the fluid we can prove, under some conditions, chaotic asymptotic behavior for suitable geometry of the circuit and heat flux or ambient temperature functions. KEYWORDS asymptotic behaviour, linear friction, thermosyphon, thermodiffusion, Soret effect, viscoelastic fluid MSC CLASSIFICATION 35B40; 35K; 35Q; 58J99; 74D05

The Role of Elasticity on Chaotic Dynamics: Insights from Mechanics, Immunology, Ecology, and Rheology

“…This, in turn, proves the existence of the inertial manifold for system (A7), employing similar techniques as in Refs. [6,14,15,28,29].…”

“…Well-Posedness and Boundedness: Global Attractor For completeness, we include the details of well-posedness and boundedness for the present model as it requires specific work, although the techniques used are similar to those in Refs. [28,29].…”