Abstract
We investigate the stability of a fluid film with power-law rheology flowing down a porous nonplanar incline with periodic undulations. A model is implemented which accounts for filtration flow through the substrate. A reduction in dimensionality in the model is achieved by exploiting the assumed thinness of the liquid film relative to the wavelength of the bottom undulations. A steady flow is obtained and its linear stability determined through the application of Floquet–Bloch theory. A nonlinear stability analysis is also carried out by calculating the evolution of the perturbed steady flow by means of numerical simulations. • An investigation of instability of film flow down an uneven porous incline. • A power-law rheological model is implemented. • Film flow is coupled with the filtration flow through the porous medium. • Combined effects of surface tension, rheology and properties of substrate determined.
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