Hydromagnetic instability of a power-law liquid film flowing down a vertical cylinder using numerical approximation approach techniques

Cheng, Po‐Jen; Liu, Kuo-Chi

doi:10.1016/j.apm.2008.03.018

Cited by 8 publications

(7 citation statements)

References 24 publications

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“…The microstructure characteristic of the power-law fluid suppresses the convective motion of the flow because the effective viscosity will increase when n increases. The results of the linear stability analysis are in agreement with those of Cheng and Liu [18] and Dandapat and Mukhopadhyay [24]. Figure 2(b) shows the temporal growth rate of a power-law fluid during spin coating at n = 0.9, 0.95, 1.0 and 1.1, respectively.…”

Section: Linear Stability Analysissupporting

confidence: 87%

“…In practice, the parameter S has a large value and  << 1, so the term  2 S is taken to be of order one [15][16][17][18]. In the present analysis, long-wave perturbation analysis is used to find out the asymptotic solutions of the above governing equation together with boundary conditions, this can be done by expanding the stream function and flow pressure in terms of a power series of  as…”

Section: Mathematical Formulationmentioning

confidence: 99%

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Surface Instabilities on a Thin Power-Law Fluid During Spin Coating

2014

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The phenomena of surface instabilities in a thin power-law fluid during spin coating are investigated. The set of Navier-Stokes equations with non-Newtonian behavior in the region of low Reynolds number serves as a mathematical description of the physical systems. Long-wave perturbation analysis is proposed to derive an evolution equation of the Ostwald de-Waele type fluid to govern the propagation of surface waves. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The amplitude of instability is determined by a Ginzburg-Landau equation. The study reveals that the degree of power-law index plays a vital role in stabilizing the film flow. The shear-thinning fluid is more unstable than the shear-thickening fluid in the stability analysis. Further, the nonlinear wave speed in the supercritical stability region decreases with increasing values of power-law index.

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Section: Linear Stability Analysissupporting

confidence: 87%

Section: Mathematical Formulationmentioning

confidence: 99%

Surface Instabilities on a Thin Power-Law Fluid During Spin Coating

2014

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“…Linear and nonlinear analyses on the stability of a thin film subjected to air shear on a free surface in the presence of a transversely applied external magnetic field of constant strength have been studied. Instead of obtaining the solutions at different orders of approximation using a power series approach [37][38][39]43], the solutions of equations arising at various orders have been straightforwardly solved [28].…”

Section: Discussionmentioning

confidence: 99%

“…In all of the above applications, considering the associated stability problem is important because it gives guidance in choosing the flow parameters for practical purposes. In this regard, in the past two decades, the emerging studies on the hydromagnetic effects have focused their attention on stability problems and on analyzing the flow characteristics [28,29,[32][33][34][35][36][37][38][39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Air-Aided Shear on a Thin Film Subjected to a Transverse Magnetic Field of Constant Strength: Stability and Dynamics

Iqbal¹

2013

ISRN Mathematical Physics

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The effect of air shear on the hydromagnetic instability is studied through (i) linear stability, (ii) weakly nonlinear theory, (iii) sideband stability of the filtered wave, and (iv) numerical integration of the nonlinear equation. Additionally, a discussion on the equilibria of a truncated bimodal dynamical system is performed. While the linear and weakly nonlinear analyses demonstrate the stabilizing (destabilizing) tendency of the uphill (downhill) shear, the numerics confirm the stability predictions. They show that (a) the downhill shear destabilizes the flow, (b) the time taken for the amplitudes corresponding to the uphill shear to be dominated by the one corresponding to the zero shear increases with magnetic fields strength, and (c) among the uphill shear-induced flows, it takes a long time for the wave amplitude corresponding to small shear values to become smaller than the one corresponding to large shear values when the magnetic field intensity increases. Simulations show that the streamwise and transverse velocities increase when the downhill shear acts in favor of inertial force to destabilize the flow mechanism. However, the uphill shear acts oppositely. It supports the hydrostatic pressure and magnetic field in enhancing films stability. Consequently, reduced constant flow rates and uniform velocities are observed.

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“…The two dimensional flow instability of non-Newtonian thin films flowing down a cylinder has also been investigated by Cheng and Liu [32][33][34] for a power-law fluid, by Cheng et al [35] and Cheng and Lai [36] for a viscoelastic Walters B fluid (with application to magnetohydrodynamics). In Moctezuma-Sánchez and Dávalos-Orozco [37] the viscoelastic Oldroyd's constitutive equation model was used to investigate the longwave linear instability of a fluid film flowing down a cylinder.…”

Section: Introductionmentioning

confidence: 97%