THE STABILITY ANALYSIS OF HEAT TRANSFER IN SATURATED LIQUID FILM OF THE SPECIAL MATERIALS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1547-1550
Author(s):  
YOULIANG CHENG ◽  
XIN LI ◽  
ZHONGYAO FAN ◽  
BOFEN YING
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Surface Tension ◽  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Relationship ◽  
Saturated Liquid ◽  
Nonlinear Surface ◽  
Isothermal Wall ◽  
The Stability

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

Nonlinear Effects on Coexistence Phenomenon in Parametric Excitation

2002 ◽  
Author(s):  
Leslie Ng ◽  
Richard Rand
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Stability Analysis ◽  
Linear Stability Analysis ◽  
Perturbation Methods ◽  
Nonlinear Effects ◽  
Free Vibrations ◽  
The Stability ◽  
Parameter Values ◽  
Two Degree Of Freedom

We investigate the effect of nonlinearites on a parametrically excited ordinary differential equation whose linearization exhibits the phenomena of coexistence. The differential equation studied governs the stability mode of vibration in an unforced conservative two degree of freedom system used to model the free vibrations of a thin elastica. Using perturbation methods, we show that at parameter values corresponding to coexistence, nonlinear terms can cause the origin to become nonlinearly unstable, even though linear stability analysis predicts the origin to be stable. We also investigate the bifurcations associated with this instability.

Lyapunov-Based Sufficient Conditions for Nonlinear Impulsive Systems

2011 ◽  
Vol 219-220 ◽  
pp. 508-512
Author(s):  
Yong Liang Gao ◽  
Xiao Wu Mu
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Invariant Set ◽  
Positive Definite ◽  
Impulsive Systems ◽  
Stability Theorems ◽  
Sufficient Conditions For Convergence ◽  
The Stability

This paper focuses on the stability analysis and invariant set stability theorems for nonlinear impulsive systems. A set of Lyapunov-based sufficient conditions are established for these convergent properties. These results do not require the Lyapunov function to be positive definite. Inequalities relating the righthandside of the differential equation and the Lyapunov function derivative are involved for these results. These inequalities make it possible to deduce properties of the functions and thus leads to sufficient conditions for convergence and stability.

Inverse-thermocapillary evaporation in a thin liquid film of self-rewetting fluid

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Elaine Lim ◽  
Tze Cheng Kueh ◽  
Yew Mun Hung
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Liquid Film ◽  
Temperature Region ◽  
Thin Liquid Film ◽  
Thermocapillary Flow ◽  
Working Fluid ◽  
Surface Tension Gradient ◽  
Thermocapillary Effect ◽  
Content Type

Purpose The present study aims to investigate the inverse-thermocapillary effect in an evaporating thin liquid film of self-rewetting fluid, which is a dilute aqueous solution (DAS) of long-chain alcohol. Design/methodology/approach A long-wave evolution model modified for self-rewetting fluids is used to study the inverse thermocapillary characteristics of an evaporating thin liquid film. The flow attributed to the inverse thermocapillary action is manifested through the streamline plots and the evaporative heat transfer characteristics are quantified and analyzed. Findings The thermocapillary flow induced by the negative surface tension gradient drives the liquid from a low-surface-tension (high temperature) region to a high-surface-tension (low temperature) region, retarding the liquid circulation and the evaporation strength. The positive surface tension gradients of self-rewetting fluids induce inverse-thermocapillary flow. The results of different working fluids, namely, water, heptanol and DAS of heptanol, are examined and compared. The thermocapillary characteristic of a working fluid is significantly affected by the sign of the surface tension gradient and the inverse effect is profound at a high excess temperature. The inverse thermocapillary effect significantly enhances evaporation rates. Originality/value The current investigation on the inverse thermocapillary effect in a self-rewetting evaporating thin film liquid has not been attempted previously. This study provides insights on the hydrodynamic and thermal characteristics of thermocapillary evaporation of self-rewetting liquid, which give rise to significant thermal enhancement of the microscale phase-change heat transfer devices.

scholarly journals Mullins–Sekerka stability analysis for melting-freezing waves in helium

1994 ◽  
Vol 5 (1) ◽  
pp. 21-37
Author(s):  
Joseph D. Fehribach
Keyword(s):  
Surface Tension ◽  
Growth Rate ◽  
Stability Analysis ◽  
Original Problem ◽  
The Other ◽  
Field Conditions ◽  
System Of Equations ◽  
Far Field ◽  
Other Hand ◽  
The Stability

This paper considers the stability of melt-solid interfaces to eigenfunction perturbations for a system of equations which describe the melting and freezing of helium. The analysis is carried out in both planar and spherical geometries. The principal results are that when the melt is freezing, under certain far-field conditions, the interface is stable in the sense of Mullins and Sekerka. On the other hand, when the solid is melting (at least when the melting is sufficiently fast), the interface is unstable. In some circumstances these instabilities are oscillatory, with amplitude and growth rate increasing with surface tension and frequency. The last section considers the original problem of Mullins and Sekerka in the present notation.

The effect of surfactant on the stability of a fluid filament embedded in a viscous fluid

1999 ◽  
Vol 382 ◽  
pp. 331-349 ◽  
Author(s):  
S. HANSEN ◽  
G. W. M. PETERS ◽  
H. E. H. MEIJER
Keyword(s):  
Surface Tension ◽  
Growth Rate ◽  
Reynolds Number ◽  
Stability Analysis ◽  
Viscous Fluid ◽  
High Elasticity ◽  
Fluid Filament ◽  
The Stability ◽  
Elasticity Number

The effect of surfactant on the breakup of a viscous filament, initially at rest, surrounded by another viscous fluid is studied using linear stability analysis. The role of the surfactant is characterized by the elasticity number – a high elasticity number implies that surfactant is important. As expected, the surfactant slows the growth rate of disturbances. The influence of surfactant on the dominant wavenumber is less trivial. In the Stokes regime, the dominant wavenumber for most viscosity ratios increases with the elasticity number; for filament to matrix viscosity ratios ranging from about 0.03 to 0.4, the dominant wavenumber decreases when the elasticity number increases. Interestingly, a surfactant does not affect the stability of a filament when the surface tension (or Reynolds) number is very large.

Influence of a spanning liquid film on the stability and buckling of a circular loop with intrinsic curvature or intrinsic twist density

2016 ◽  
Vol 23 (1) ◽  
pp. 43-66 ◽  
Author(s):  
Tuan Hoang ◽  
Eliot Fried
Keyword(s):  
Surface Tension ◽  
Liquid Film ◽  
Flexural Rigidity ◽  
Torsional Rigidity ◽  
Stable Solution ◽  
Variational Model ◽  
Intrinsic Curvature ◽  
Buckling Modes ◽  
Out Of Plane ◽  
The Stability

A variational model is used to study the behavior of a flexible but inextensible loop spanned by a liquid film, with the objective of explaining the stability and buckling of flat circular configurations. Loops made from filaments with intrinsic curvature and/or intrinsic twist density are considered, but attention is restricted to filaments with circular cross sections and uniform mechanical properties. Loops made with intrinsic curvature but no intrinsic twist density exhibit in-plane and out-of-plane buckling modes corresponding to stable solution branches that bifurcate from the branch of flat circular solutions and out-of-plane buckling occurs at a lower value of the dimensionless surface tension of the liquid film than does in-plane buckling. Additionally, however, the destabilizing influence of the intrinsic curvature can be countered by increasing the torsional rigidity relative to the flexural rigidity. For a loop with both intrinsic curvature and intrinsic twist density, only one branch of stable solutions bifurcates from the flat circular solution branch, the in-plane and out-of-plane buckling modes are intertwined, and bifurcation occurs at a value of the dimensionless surface tension less than that governing the behavior of loops made from filaments that are intrinsically rectilinear. Moreover, increasing the torsional rigidity relative to the flexural rigidity has no or little stabilizing effect if the loop is either too short or too long and, in contrast to what occurs for loops with only intrinsic curvature, if the intrinsic twist density is sufficiently large then the destabilizing influence of the intrinsic curvature cannot be countered by increasing the torsional rigidity relative to the flexural rigidity, regardless of the length of the loop.

Instability and Frontal Breakup in Super-Meniscus Films

1996 ◽  
Vol 464 ◽  
Author(s):  
Dawn E. Kataoka ◽  
Sandra M. Troian
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Temperature Distribution ◽  
Liquid Film ◽  
Linear Stability Analysis ◽  
Surface Coverage ◽  
Flow Behavior ◽  
Leading Edge ◽  
Nonuniform Temperature ◽  
Unstable Flow

ABSTRACTSurface tension gradients created by a nonuniform temperature distribution in athin liquid film can force vertical spreading beyond the equilibrium meniscus [1]. Experiments designed to probe the flow behavior of super-meniscus films have shown that the leading edge can either spread uniformly with complete surface coverage or become corrugated and breakupinto long slender rivulets. We show that within linear stability analysis, both the conditions for unstable flow and the most unstable wavelength compare favorably with recent experiments reported in the literature.

Convective instability in liquid pools heated from below

1971 ◽  
Vol 47 (4) ◽  
pp. 779-787 ◽  
Author(s):  
Harvey J. Palmer ◽  
John C. Berg
Keyword(s):  
Surface Tension ◽  
Heat Flux ◽  
Stability Analysis ◽  
Convective Instability ◽  
Temperature Drop ◽  
Stability Limit ◽  
Liquid Pool ◽  
Silicone Oils ◽  
Liquid Pools ◽  
The Stability

The linear hydrodynamic stability analysis of liquid pools heated from below combining surface tension and buoyancy effects as presented by Nield (1964) is confirmed by experiment for a series of silicone oils. The experimental method used is an adaptation of the Schmidt–Milverton technique, in which the stability limit is located by the change of slope in the plot of heat flux versus temperature drop across the liquid pool.

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