# On the Modeling and Control of Coupled Multi-Loop Thermosyphons

## Document Type

Conference Proceeding

## Publication Date

1-29-2011

## Publication Title

Applications of Mathematics and Computer Engineering: Proceedings of the American Conference on Applied Mathematics

## ISBN

978-960-474-270-7

## ISSN

1792-7714

## Abstract

This paper presents a one-dimensional model for natural convection in coupled multi-loop thermosyphons. The physical model is governed by a system of Navier-Stokes equations, which are reduced to coupled systems of Lorenz equations via the Galerkin method. The simulations reveal different stages of flow of the Rayleigh number increases, e.g., from heat conduction, steady convective flow, to chaotic time-dependent flow. The control objective is either stabilized the flow in each loop at one its equilibrium points or track a reference signal in the chaotic range of the Rayleigh number. The controller design is based on proportional and integral (PI) control principles. The design can be easily implemented because the feedback state is measurable.

## Recommended Citation

Wu, Yan.
2011.
"On the Modeling and Control of Coupled Multi-Loop Thermosyphons."
*Applications of Mathematics and Computer Engineering: Proceedings of the American Conference on Applied Mathematics*, Alexander Zemliak, Nikos Mastorakis (Ed.): 105-110 Puerto Morelos, Mexico: World Scientific and Engineering Academy and Society Press.
source: http://www.wseas.us/e-library/conferences/2011/Mexico/CEMATH/CEMATH-17.pdf isbn: 978-960-474-270-7

https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/239