Effects of viscosity variation on the stability of film flow down heated or cooled inclined surfaces: Long-wavelength analysis

1985 ◽  
Vol 28 (11) ◽  
pp. 3207 ◽  
Author(s):  
D. Goussis ◽  
R. E. Kelly
Keyword(s):  
Film Flow ◽  
Long Wavelength ◽  
Inclined Surfaces ◽  
Viscosity Variation ◽  
The Stability

Bifurcation and stability analysis of stagnation points for an asymmetric peristaltic transport

2020 ◽  
Vol 98 (2) ◽  
pp. 172-182 ◽  
Author(s):  
Kaleem Ullah ◽  
Nasir Ali
Keyword(s):  
Flow Field ◽  
Amplitude Ratio ◽  
Nonlinear Differential Equations ◽  
Global Bifurcation ◽  
Flow Region ◽  
Peristaltic Transport ◽  
Trapping Region ◽  
Long Wavelength ◽  
Stagnation Points ◽  
The Stability

This paper investigates the streamline topologies and stability of stagnation points and their bifurcations for an asymmetric peristaltic flow. The asymmetry of channel is due to the propagation of peristaltic waves with different phases and amplitudes on the flexible channel walls. An exact analytic solution of the flow problem subject to the constraints of low Reynolds number and long wavelength is obtained in wave frame of reference moving with wave velocity. A system of nonlinear differential equations is established to locate and classify the stagnation points in the flow domain. Different flow situations, manifested in the flow field, are categorized as: backward flow, trapping, and augmented flow. The transition from one situation to the other corresponds to bifurcation, which is explored graphically through local and global bifurcation diagrams. This analysis discloses the stability status of stagnation points and ranges of involved parameters in which various flow conditions appear in the flow field. It is concluded that the trapping in an asymmetric peristaltic transport can be reduced by increasing the phase difference of the channel walls. It is also found that the augmented flow region shrinks and the trapping region expands by increasing the amplitude ratio of the channel walls.

STABILITY ANALYSIS OF THE THIN POWER LAW LIQUID FILM FLOWING DOWN ON A VERTICAL CYLINDER

2006 ◽  
Vol 30 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Po-Jen Cheng ◽  
Kuo-Chi Liu
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Flow Index ◽  
Free Film ◽  
Long Wave ◽  
Lateral Curvature ◽  
The Stability ◽  
Film Interface

The paper investigates the stability theory of a thin power law liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized linear kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The analysis results also indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

scholarly journals Modified Kawahara equation within a fractional derivative with non-singular kernel

2018 ◽  
Vol 22 (2) ◽  
pp. 789-796 ◽  
Author(s):  
Devendra Kumar ◽  
Jagdev Singh ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Derivative ◽  
Numerical Solution ◽  
Water Waves ◽  
Iterative Scheme ◽  
Singular Kernel ◽  
Kawahara Equation ◽  
Long Wavelength ◽  
Exponential Kernel ◽  
The Stability ◽  
Linear Water Waves

The article addresses a time-fractional modified Kawahara equation through a fractional derivative with exponential kernel. The Kawahara equation describes the generation of non-linear water-waves in the long-wavelength regime. The numerical solution of the fractional model of modified version of Kawahara equation is derived with the help of iterative scheme and the stability of applied technique is established. In order to demonstrate the usability and effectiveness of the new fractional derivative to describe water-waves in the long-wavelength regime, numerical results are presented graphically.

On the collective instability of salt fingers

1981 ◽  
Vol 110 ◽  
pp. 195-207 ◽  
Author(s):  
Judith Y. Holyer
Keyword(s):  
Prandtl Number ◽  
Internal Wave ◽  
Stability Criterion ◽  
Long Wavelength ◽  
Salt Fingers ◽  
The Stability

In this paper we consider the stability of salt fingers to long wavelength internal wave perturbations. The Prandtl number of the fluid is assumed to be large, but the ratio of the two diffusivities (KS/KT) is allowed to be any size provided that KS < KT. This problem was first considered by Stern (1969), where several untested assumptions were made about the motion. Here we use a two-scale approach to separate the salt finger motions from the long-scale internal wave perturbations and to obtain the stability criterion. This collective instability of salt fingers succeeds in transferring energy from the small salt finger scales to the long internal wave scales.

Stability of strong electromagnetic waves in overdense plasmas against long-wavelength perturbations

1985 ◽  
Vol 33 (2) ◽  
pp. 285-301 ◽  
Author(s):  
F. J. Romeiras ◽  
G. Rowlands
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves ◽  
Electromagnetic Waves ◽  
Modulation Depth ◽  
Longitudinal Direction ◽  
Transverse Component ◽  
Ion Density ◽  
Long Wavelength ◽  
The Stability ◽  
Two Parameters

We consider the stability against long-wavelength small parallel perturbations of a class of exact standing wave solutions of the equations that describe an unmagnetized relativistic overdense cold electron plasma. The main feature of these nonlinear waves is a circularly polarized transverse component of the electric field periodically modulated in the longitudinal direction. Using an analytical method developed by Rowlands we obtain a dispersion relation valid for long-wavelength perturbations. This dispersion relation is a biquadratic equation in the phase velocity of the perturbations whose coefficients are very complicated functions of the two parameters used to define the nonlinear waves: the normalized ion density and a quantity related to the modulation depth. This dispersion relation is discussed for the whole range of the two parameters revealing, in particular, the existence of a region in parameter space where the nonlinear waves are stable.

Evaluation of Ar-Diluted Silane PECVD for Thin Film Si:H Based Solar Cells

2004 ◽  
Vol 808 ◽  
Author(s):  
J. A. Anna Selvan ◽  
Yuan-Min Li ◽  
Liwei Li ◽  
Alan E. Delahoy
Keyword(s):  
Solar Cells ◽  
Spectral Response ◽  
Nanocrystalline Silicon ◽  
Thin Layers ◽  
Dilution Method ◽  
Critical Question ◽  
Long Wavelength ◽  
Hydrogen Dilution ◽  
Porous Microstructure ◽  
The Stability

ABSTRACTDilution by Ar of silane plasma has been reported to increase the stability of a-Si:H films. A critical question is whether Ar diluted i-layers offer higher stabilized solar cell efficiencies than the conventional hydrogen dilution method. We have fabricated a-Si:H p-i-n solar cells with RF-PECVD i-layers by Ar dilution of silane. Ar dilution ratio (ADR, Ar/SiH4), RF power,pressure, and i-layer thickness were varied. At low ADR < 20, such solar cells show comparable initial efficiencies and stability as those devices having H2-diluted i-layers of similar thickness. For cells made with ADR > 20, the initial efficiency decreases dramatically with further increase in Ar dilution, and light soaking causes only mild changes in efficiencies. The stabilized efficiencies of cells made with high ADR are inferior to the cells produced with low ADR or cells prepared by H2 dilution. Further, Voc of solar cells made with high ADR (> 50) decreases substantially in ambient, indicating a porous microstructure susceptible to oxidation. While thermal annealing improves the Voc, a full recovery of Voc is made by accelerated light soaking.The combination of high power and high ADR can lead to nanocrystalline silicon (nc-Si:H) growth, although nucleation is much more difficult to attain by the Ar dilution method compared to hydrogen dilution. We have succeeded in fabricating p-i-n solar cells with nc-Si:H i-layers prepared by the Ar dilution approach. The double dilution by Ar and hydrogen of silane (Ar+H2+SiH4) can result in nc-Si:H i-layers with enhanced long wavelength spectral response compared to devices incorporating nc-Si:H i-layers grown by H2 dilution only. The nc-Si:H solar cells with Ar+H2 diluted i-layers exhibit no light-induced degradation.Using energetic Ar-rich plasma, in a process much simpler than the traditional nc-Si:H technique, doped a-Si:H thin layers can be prepared to form excellent tunnel junctions for multi-junction solar cells. We demonstrate such a novel, non-contaminating tunnel junction in tandem a-Si/a-Si and a-Si/nc-Si solar cells entirely fabricated in a single-chamber RF-PECVD system.

scholarly journals An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lee Ken Yap ◽  
Fudziah Ismail ◽  
Norazak Senu
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Collocation Method ◽  
Film Flow ◽  
Direct Solution ◽  
Thin Film Flow ◽  
Block Method ◽  
Third Order ◽  
Block Form ◽  
The Stability

The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form to provide the approximation at five points concurrently. The stability properties of the block method are investigated. Some numerical examples are tested to illustrate the efficiency of the method. The block hybrid collocation method is also implemented to solve the nonlinear Genesio equation and the problem in thin film flow.

scholarly journals The stability of accretion tori - I. Long-wavelength modes of slender tori

1986 ◽  
Vol 221 (2) ◽  
pp. 339-364 ◽  
Author(s):  
P. Goldreich ◽  
J. Goodman ◽  
R. Narayan
Keyword(s):  
Long Wavelength ◽  
The Stability
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