Mathematical Problems in Engineering 
Volume 2007 (2007), Article ID 81514, 24 pages
doi:10.1155/2007/81514
Research Article

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

Xiaoling He

 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

Recommended by José Manoel Balthazar

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.