Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 81514, 24 pages
Successive Bifurcation Conditions of a Lorenz-Type Equation for the Fluid Convection Due to the Transient Thermal Field
Department of Materials Engineering, College of Engineering and Applied Science, University of Wisconsin-Milwaukee, 3200 North Cramer Street, P.O. Box 784, Milwaukee, WI 53201-784, USA
Received 13 October 2006; Revised 13 February 2007; Accepted 7 June 2007
Academic Editor: José Manoel Balthazar
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.
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.