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Stability Analysis of A Thin Micropolar Fluid Flowing on A Rotating Circular Disk

Published online by Cambridge University Press:  31 March 2011

C. K. Chen ,
M. C. Lin  and
C. I. Chen
C. K. Chen*
Affiliation:
Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
M. C. Lin
Affiliation:
Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences Kaohsiung, Taiwan 80778, R.O.C.
C. I. Chen
Affiliation:
Department of Industrial Engineering and Management, I-Shou UniversityKaohsiung County, Taiwan 84041, R.O.C.
*
* Professor, corresponding author
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Abstract

The stability analysis of a thin micropolar fluid flowing on a rotating circular disk is investigated numerically. The target is restricted to some neighborhood of critical value in the linear stability analysis. First, a generalized nonlinear kinematic model is derived by the long wave perturbation method. The method of normal mode is applied to the linear stability. After the weakly nonlinear dynamics of a film flow is studied by using the method of multiple scales, the Ginzburg-Landau equation is determined to discuss the necessary condition in terms of the various states of subcritical stability, subcritical instability, supercritical stability, and supercritical explosion for the existence of such flow pattern. The modeling results indicate that the rotation number and the radius of circular disk play the significant roles in destabilizing the flow. Furthermore, the micropolar parameter K serves as the stabilizing factor in the thin film flow.

Keywords

Nonlinear stabilityMicropolar fluidGinzburg-Landau equation
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 1 , March 2011 , pp. 95 - 105
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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