Proceedings ArticleDOI
Weakly Nonlinear Stability Analysis of a Non-Uniformly Heated Non-Newtonian Falling Film
R. Usha,I. Mohammed Rizwan Sadiq +1 more
- pp 1661-1670
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TLDR
In this paper, a thin liquid layer of a non-Newtonian film falling down an inclined plane that is subjected to non-uniform heating has been considered and a nonlinear evolution equation is derived by applying the long-wave theory and the equation governs the evolution of a power-law film flowing down a inclined plane.Abstract:
A thin liquid layer of a non-Newtonian film falling down an inclined plane that is subjected to non-uniform heating has been considered. The temperature of the inclined plane is assumed to be linearly distributed and the case when the temperature gradient is positive or negative is investigated. The film flow is influenced by gravity, mean surface-tension and thermocapillary force acting along the free surface. The coupling of thermocapillary instability and surface-wave instabilities is studied for two-dimensional disturbances. A non-linear evolution equation is derived by applying the long-wave theory and the equation governs the evolution of a power-law film flowing down an inclined plane. The linear stability analysis shows that the film flow system is stable when the plate temperature is decreasing in the downstream direction while it is less stable for increasing temperature along the plate. Weakly non-linear stability analysis using the method of multiple scales has been investigated and this leads to a secular equation of the Ginzburg-Landau type. The analysis shows that both supercritical stability and subcritical instability are possible for the film flow system. The results indicate the existence of finite-amplitude waves and the threshold amplitude and non-linear speed of these waves are influenced by thermocapillarity. The results for the dilatant as well as pseudoplastic fluids are obtained and it is observed that the result for the Newtonian model agrees with the available literature report. The influence of non-uniform heating of the film flow system on the stability of the system is compared with the stability of the corresponding uniformly heated film flow system.Copyright © 2007 by ASMEread more
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Journal ArticleDOI
Instabilities in a liquid film flow over an inclined heated porous substrate
TL;DR: In this paper, an evolution equation for the local film thickness for two-dimensional disturbances is derived to analyze the effect of long-wave instabilities, and the parameters governing the film flow system and the porous substrate strongly influence the wave forms and their amplitudes and hence the stability of the fluid.
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Falling liquid films on longitudinal grooved geometries: Integral boundary layer approach
TL;DR: In this paper, a falling thin liquid film on a substrate with complex topography is modeled using a three equation integral boundary layer system and linear stability and nonlinear dynamics of the film in the framework of this model are studied on a topography with sinusoidal longitudinal grooves aligned parallel in the direction of the main flow.
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Air-Aided Shear on a Thin Film Subjected to a Transverse Magnetic Field of Constant Strength: Stability and Dynamics
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References
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Stability of Liquid Flow down an Inclined Plane
TL;DR: In this paper, the stability of a liquid layer flowing down an inclined plane is investigated, and a new perturbation method is used to furnish information regarding stability of surface waves for three cases: the case of small wavenumbers, of small Reynolds numbers, and of large wavenifications.
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Wave evolution on a falling film
TL;DR: In this paper, a review of wave evolution on a free-falling vertical film is presented, focusing on the nonlinear mechanisms behind these secondary transitions, as well as the dynamics on an inclined plane.
MonographDOI
Interfacial Phenomena and Convection
TL;DR: Interfacial Phenomena and Convection as mentioned in this paper is a self-contained monograph that examines a rich variety of interfacial phenomena in which interfaces pay a crucial role.
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Long-Wave Instabilities in a Non-Newtonian Film on a Nonuniformly Heated Inclined Plane
I. Mohammed Rizwan Sadiq,R. Usha +1 more