Instabilities in a liquid film flow over an inclined heated porous substrate

Stability of a thin viscous Newtonian fluid draining down a uniformly heated porous inclined plane is examined. The long-wave linear stability analysis is performed within the generic Orr-Sommerfeld framework both theoretically and numerically. An evolution equation for the local film thickness for...

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Bibliographic Details
Published in:Chemical engineering science 2010-08, Vol.65 (15), p.4443-4459
Main Authors: Sadiq, I. Mohammed Rizwan, Usha, R., Joo, Sang Woo
Format: Article
Language:English
Subjects:
Amplitudes
Applied sciences
Chemical engineering
Disturbances
Drainage
Exact sciences and technology
Fluid mechanics
Heat and mass transfer. Packings, plates
Heat transfer
Instability
Mathematical analysis
Permeability
Porous media
Stability
Stability analysis
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Summary:Stability of a thin viscous Newtonian fluid draining down a uniformly heated porous inclined plane is examined. The long-wave linear stability analysis is performed within the generic Orr-Sommerfeld framework both theoretically and numerically. An evolution equation for the local film thickness for two-dimensional disturbances is derived to analyze the effect of long-wave instabilities. 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. The long-time wave forms are either time-independent wave forms that propagate or time-dependent modes that oscillate slightly in the amplitude. The role of permeability and Marangoni number is to increase the amplitude of the disturbance leading to the destabilization state of the film flow system. The permeability of the porous medium promotes the oscillatory behavior.
ISSN:0009-2509
1873-4405
DOI:10.1016/j.ces.2010.04.005