Finite-Amplitude Long-Wave Instability of a Thin Power-Law Liquid Film Flowing Down a Vertical Column in a Magnetic Field

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
Po-Jen Cheng
Keyword(s):  
Magnetic Field ◽  
Liquid Film ◽  
Power Law ◽  
Vertical Cylinder ◽  
Finite Amplitude ◽  
Flow Index ◽  
Vertical Column ◽  
Electrically Conductive ◽  
Long Wave ◽  
The Stability

The long-wave perturbation method is employed to investigate the nonlinear hydromagnetic stability of a thin electrically conductive power-law liquid film flowing down a vertical cylinder. In contrast to most previous studies presented in literature, the solution scheme employed in this study is based on a numerical approximation approach rather than an analytical method. The modeling results reveal that the stability of the film flow system is weakened as the radius of the cylinder is reduced. However, the flow stability can be enhanced by increasing the intensity of the magnetic field and the flow index.

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.

Long-Wave Perturbation Method to Investigate Nonlinear Stability of the Thin Power Law Liquid Film Flowing Down on a Vertical Cylinder

2008 ◽  
Vol 24 (3) ◽  
pp. 241-252 ◽  
Author(s):  
P. -J. Cheng ◽  
K. -C. Liu
Keyword(s):  
Liquid Film ◽  
Perturbation Method ◽  
Power Law ◽  
Film Flow ◽  
Multiple Scales ◽  
Vertical Cylinder ◽  
Flow Index ◽  
Wave Perturbation ◽  
Stability Diagrams ◽  
Long Wave

ABSTRACTThe influence of both the flow index and the cylinder size on the nonlinear hydrodynamic stability of a thin power law liquid film flowing down along the surface of a vertical cylinder is investigated. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with a free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weakly nonlinear dynamics of the film flow for stability analysis. The stability criteria are discussed theoretically and numerically and stability diagrams are obtained. The modeling results 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.

Rupture of Thin Power-Law Liquid Film on a Cylinder

2000 ◽  
Vol 68 (2) ◽  
pp. 294-297 ◽  
Author(s):  
Rama Subba Reddy Gorla
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Body Force ◽  
Finite Amplitude ◽  
Rupture Process ◽  
Dynamic Rupture ◽  
Balance Equations ◽  
Initial Value ◽  
Power Law Exponent ◽  
The Stability

The dynamic rupture process of a thin power-law type non-Newtonian liquid film on a cylinder has been analyzed by investigating the stability to finite amplitude disturbances. The dynamics of the liquid film is formulated using the balance equations including a body force term due to van der Waals attractions. The governing equation for the film thickness was solved by finite difference method as part of an initial value problem for spatial periodic boundary conditions. A decrease in the cylinder radius will induce a stronger lateral capillary force and thus will accelerate the rupture process. The influence of the power-law exponent on rupture is discussed.

Stability Analysis on Viscous Magnetic Fluid Film Flowing Down Along a Vertical Cylinder

2007 ◽  
Vol 23 (2) ◽  
pp. 127-134 ◽  
Author(s):  
P.-J. Cheng ◽  
K.-C. Liu
Keyword(s):  
Film Flow ◽  
Vertical Cylinder ◽  
Fluid Film ◽  
Electrically Conductive ◽  
Free Film ◽  
Long Wave ◽  
Lateral Curvature ◽  
The Stability ◽  
The Magnetic Field ◽  
Film Interface

AbstractThe paper investigates the hydromagnetic stability theory of a thin electrically conductive fluid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The modeling results display that 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. It is also observed that by increasing the effect of the magnetic field and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

The instability of a pinched fluid with a longitudinal magnetic field

1958 ◽  
Vol 245 (1241) ◽  
pp. 222-237 ◽  
Keyword(s):  
Magnetic Field ◽  
Longitudinal Magnetic Field ◽  
Short Wave ◽  
Longitudinal Field ◽  
Plasma Equilibrium ◽  
Azimuthal Magnetic Field ◽  
Long Wave ◽  
Pinched Plasma ◽  
Pinch Current ◽  
The Stability

The stability of a pinched plasma equilibrium with a longitudinal magnetic field superimposed on the characteristic azimuthal magnetic field of the pinch current is studied theoretically. The linearized solutions are developed as helical perturbations of the plasma surface, and the behaviour of these is given for the different cases of uniform longitudinal, longitudinal field zero inside the plasma, and for helices of the same and opposite sense to the helix which describes the total magnetic field. Approximately, the conclusions are: that the longitudinal field has the effect of stabilizing short-wave perturbations, but that some long-wave perturbations remain unstable no matter how large the externally imposed longitudinal magnetic field.

Hydromagnetic stability of a thin electrically conducting fluid film flowing down the outside surface of a long vertically aligned column

2009 ◽  
Vol 223 (2) ◽  
pp. 415-426 ◽  
Author(s):  
P-J Cheng
Keyword(s):  
Magnetic Field ◽  
Multiple Scales ◽  
Vertical Cylinder ◽  
Conducting Fluid ◽  
Fluid Film ◽  
Electrically Conducting ◽  
Free Film ◽  
Electrically Conducting Fluid ◽  
Non Linear ◽  
The Stability

This article considers the stability of a thin electrically conducting fluid film flowing down the outer surface of a long vertical cylinder in the presence of an applied magnetic field. Using the long-wave perturbation method to solve the generalized non-linear kinematic equations with free film interface, the normal mode approach is first used to compute the linear stability solution. The method of multiple scales is then used to obtain the weak non-linear dynamics. The results indicate that both subcritical instability and supercritical stability conditions are possible. The degree of instability in the film flow is intensified by the lateral curvature of the cylinder. The results also show that increasing the strength of the magnetic field tends to enhance the stability.

Hydromagnetic Stability Analysis of a Film Coating Flow Down a Rotating Vertical Cylinder

2011 ◽  
Vol 27 (1) ◽  
pp. 27-36 ◽  
Author(s):  
P.-J. Cheng ◽  
K.-C. Liu ◽  
D. T. W. Lin
Keyword(s):  
Liquid Film ◽  
Thin Liquid Film ◽  
Vertical Cylinder ◽  
Film Coating ◽  
Rossby Number ◽  
Free Film ◽  
Coating Flow ◽  
The Stability ◽  
Film Flows ◽  
The Magnetic Field

ABSTRACTThe influence of both the Rossby number and the Hartmann number on the hydromagnetic stability of a thin liquid film flowing down along the surface of a vertical cylinder is investigated. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with a free film interface. The normal mode approach is used to compute the stability solution for the film flow. The modeling results indicate that the stability of the liquid film is enhanced by increasing the strength of the magnetic field or reducing the speed at which the cylinder rotates. By contrast, the flow becomes relatively more unstable as the cylinder radius is increased at larger values of the Rossby number. Notably, this finding is the opposite of that observed for film flows along a stationary vertical cylinder.

Weakly Nonlinear Stability Analysis of Condensate/Evaporating Power-Law Liquid Film Down an Inclined Plane

2003 ◽  
Vol 70 (6) ◽  
pp. 915-923 ◽  
Author(s):  
R. Usha ◽  
B. Uma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Nonlinear Stability ◽  
Flow System ◽  
Nonlinear Stability Analysis ◽  
Power Law Fluid ◽  
Inclined Plane ◽  
Weakly Nonlinear ◽  
The Stability ◽  
Power Law Index

Weakly nonlinear stability analysis of thin power-law liquid film flowing down an inclined plane including the phase change effects at the interface has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear stability solution and the nonlinear stability solution for the film flow system. The results show that both the supercritical stability and subcritical instability are possible for condensate, evaporating and isothermal power-law liquid film down an inclined plane. The stability characteristics of the power-law liquid film show that isothermal and evaporating films are unstable for any value of power-law index ‘n’ while there exists a critical value of power-law index ‘n’ for the case of condensate film above which condensate film flow system is always stable. Thus, the results of the present analysis show that the mass transfer effects play a significant role in modifying the stability characteristics of the non-Newtonian power-law fluid flow system. The condensate (evaporating) power-law fluid film is more stable (unstable) than the isothermal power-law fluid film flowing down an inclined plane.

On the stability of nonlinear magneto-sonic waves in a collisionless plasma

1973 ◽  
Vol 10 (3) ◽  
pp. 459-468 ◽  
Author(s):  
V. V. Demchenko ◽  
A. M. Hussein
Keyword(s):  
Magnetic Field ◽  
Collisionless Plasma ◽  
Interaction Space ◽  
Finite Amplitude ◽  
Initial Pulse ◽  
Sonic Wave ◽  
Sonic Waves ◽  
The Stability

The stability of a magneto-sonic wave of small (but finite) amplitude, propagating in a low- β plasma across a magnetic field, is investigated. It is shown that such a wave is unstable with respect to parametric splitting into many satellite waves. Wavenumbers of the satellite waves differ from that of the original magneto-sonic wave. Thus, the sateffite waves leave an interaction space, and form oscillating ‘tails ’ in front of and behind the initial pulse.

Controlling the Power-Law Fluid Flow and Heat Transfer Under the External Magnetic Field Using the Flow Index and the Hartmann Number

2019 ◽  
Vol 17 (03) ◽  
pp. 1850143
Author(s):  
Cansu Evcin ◽  
Ömür Uğur ◽  
Münevver Tezer-Sezgi̇n
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Power Law ◽  
Hartmann Number ◽  
Mixed Finite Elements ◽  
Mhd Flow ◽  
Momentum Equation ◽  
Flow Index ◽  
Fluid Viscosity ◽  
Square Duct

The direct and optimal control solution of laminar fully developed, steady Magnetohydrodynamics (MHD) flow of an incompressible, electrically conducting power-law non-Newtonian fluid in a square duct is considered with the heat transfer. The fluid is subjected to an external uniform magnetic field as well as a constant pressure gradient. The apparent fluid viscosity is both a function of the unknown velocity and the flow index which makes the momentum equation nonlinear. Viscous and Joule dissipation terms are also included. The direct problem is solved by using Galerkin finite element method (FEM) with mixed finite elements and the control problem approach is the discretize-then-optimize procedure. The control formulations with the flow index parameter and the Hartmann number are given to regain the desired velocity profile and temperature isolines of the MHD flow.

Sign in / Sign up

Export Citation Format

Share Document