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 with in 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 amplitude sand hence the stability of the fluid. The long-time waveforms are either time-independent wave forms that propagate or time-dependent modes that oscillates lightly 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. (C) 2010 Elsevier Ltd. All rights reserved.