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A long-wave evolution equation is derived using an asymptotic analysis, and the linear stability of a viscoelastic film flowing along the direction of parallel grooves over a uniformly heated topography is studied. A numerical approach adopting spectral collocation technique is used to demarcate the stable and unstable flow regimes. The combined influence of thermocapillarity and viscoelasticity on the films stability is analyzed. By accounting the bottom topography comprising longitudinal gutters, the possibilities of regulating the film dynamics under iso- and nonisothermal conditions and/or optimizing design structure of an apparatus for desirable flow outcomes have been focussed

Influence of Temperature Gradient on the Stability of a Viscoelastic Film with Gradually Fading Memory over a Topography with Ridges and Furrows