Journal ArticleDOI
Thin Newtonian film flow down a porous inclined plane: Stability analysis
I. Mohammed Rizwan Sadiq,R. Usha +1 more
TLDR
In this article, a nonlinear evolution equation for the thickness of a thin Newtonian fluid layer on a porous inclined plane is obtained, assuming that the flow through the porous medium is governed by Darcy's law.Abstract:
The flow of a thin Newtonian fluid layer on a porous inclined plane is considered. Applying the long-wave theory, a nonlinear evolution equation for the thickness of the film is obtained. It is assumed that the flow through the porous medium is governed by Darcy’s law. The critical conditions for the onset of instability of a fluid layer flowing down an inclined porous wall, when the characteristic length scale of the pore space is much smaller than the depth of the fluid layer above, are obtained. The results of the linear stability analysis reveal that the film flow system on a porous inclined plane is more unstable than that on a rigid inclined plane and that increasing the permeability of the porous medium enhances the destabilizing effect. A weakly nonlinear stability analysis by the method of multiple scales shows that there is a range of wave numbers with a supercritical bifurcation, and a range of larger wave numbers with a subcritical bifurcation. Numerical solution of the evolution equation in a...read more
Citations
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Journal ArticleDOI
A falling film down a slippery inclined plane
TL;DR: In this paper, a gravity-driven film flow on a slippery inclined plane is considered within the framework of long wave and boundary layer approximations, and two coupled depth-averaged equations are derived in terms of the local flow rate and the film thickness H (x,t).
Journal ArticleDOI
Effects of inertia and surface tension on a power-law fluid flowing down a wavy incline
Christian Heining,Nuri Aksel +1 more
TL;DR: In this paper, a thin film of a power-law liquid flowing down an inclined wall with sinusoidal topography is considered and an integral boundary-layer model for the film thickness and flow rate is derived.
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.
Journal ArticleDOI
Evaluation of heat irreversibility in couple stress falling liquid films along heated inclined substrate
Samuel O. Adesanya,Adeniyi Samson Onanaye,Olalere G. Adeyemi,Mohammad Rahimi-Gorji,Mohammad Rahimi-Gorji,Ibrahim M. Alarifi +5 more
TL;DR: In this article, the analysis of entropy generation in a gravity-aided thin couple stress liquid film in an inclined heated substrate is investigated, where the thin substrate layer is assumed to be porous and governed by Darcy law.
References
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Journal ArticleDOI
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