Successive Bifurcation Conditions of a Lorenz-Type Equation for the Fluid Convection Due to the Transient Thermal Field

He, Xiaoling

doi:https://doi.org/10.1155/2007/81514

Mathematical Problems in Engineering

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Dynamics and Control in Sciences and Engineering

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Research Article | Open Access

Volume 2007 | Article ID 081514 | https://doi.org/10.1155/2007/81514

Successive Bifurcation Conditions of a Lorenz-Type Equation for the Fluid Convection Due to the Transient Thermal Field

Xiaoling He¹

Academic Editor: José Manoel Balthazar

Received13 Oct 2006

Revised13 Feb 2007

Accepted07 Jun 2007

Published05 Aug 2007

Abstract

This paper investigates the convection flow between the two parallel plates in a fluid cell subject to the transient thermal field. We use the modal approximations similar to that of the original Lorenz model to obtain a generalized Lorenz-type model for the flow induced by the transient thermal field at the bottom plate. This study examines the convection flow bifurcation conditions in relation to the transient temperature variations and the flow properties. We formulated successive bifurcation conditions and illustrated the various flow behaviors and their steady-state attractors affected by the thermal field functions and fluid properties.

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Copyright

Copyright © 2007 Xiaoling He. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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