Finite-dimensional asymptotic behavior in a thermosyphon including the Soret effect

Abstract

We analyse the dynamics of a fluid transporting a soluble substance in the interior of a closed loop of arbitrary geometry and subjected to the action of gravity and natural convection. After obtaining the governing equations and analysing the well posedness of the system we prove the existence of a global attractor. Finally, using inertial manifold techniques, we obtain an explicit reduced system of ODE's that describes the asymptotic behaviour of the full system