Fast Solutions for Large Reynold’s Number in a Closed-Loop Thermosyphon with Binary Fluid

Abstract

In this work, we analyze the asymptotic behavior of the solutions for a thermosyphon model where a binary fluid is considered, a fluid containing a soluble substance, and the Reynold’s number is large. The presented results are a generalization, in some sense, of the results for a fluid with only one component provided in Velázquez 1994 and RodrÍguez-Bernal and Van Vleck 1998. We characterize the conditions under which a fast time-dependent solution exits and it is attracted towards a fast stationary solution as the Reynold’s number tends to infinity. Numerical experiments were performed in order to illustrate the theoretical results. Using numerical simulations, we found fast time-dependent solutions close enough to the fast stationary one for certain values of the parameters.

Keywords

• asymptotic behavior
• thermosyphon
• Reynold’s number
• Soret effect
• stationary solutions