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Hydromagnetic Stability of a Thin Viscoelastic Magnetic Fluid on Coating Flow Using Landau Equation

Published online by Cambridge University Press:  23 June 2016

C.-K. Chen  and
M.-C. Lin
C.-K. Chen
Affiliation:
Department of Mechanical EngineeringNational Cheng Kung UniversityTainan, Taiwan
M.-C. Lin*
Affiliation:
Department of Mechanical EngineeringNational Kaohsiung University of Applied SciencesKaohsiung, Taiwan
*
*Corresponding author ([email protected])
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Abstract

This paper investigates the weakly nonlinear stability of a thin axisymmetric viscoelastic fluid with hydromagnetic effects on coating flow. The governing equation is resolved using long-wave perturbation method as part of an initial value problem for spatial periodic surface waves with the Walter's liquid B type fluid. The most unstable linear mode of a film flow is determined by Ginzburg-Landau equation (GLE). The coefficients of the GLE are calculated numerically from the solution of the corresponding stability problem on coating flow. The effect of a viscoelastic fluid under an applied magnetic field on the nonlinear stability mechanism is studied in terms of the rotation number, Ro, viscoelastic parameter, k, and the Hartmann constant, m. Modeling results indicate that the Ro, k and m parameters strongly affect the film flow. Enhancing the magnetic effects is found to stabilize the film flow when the viscoelastic parameter destabilizes the one in a thin viscoelastic fluid.

Keywords

Hydromagnetic stabilityGinzburg-Landau equationCoating flow
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 5 , October 2016 , pp. 643 - 651
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2016 

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