| Summary: | Motivated by the lubrication approximation application from the small-scale activity in dermatology to the big-scale process in coating industry involving flow driven by shear stress, a mathematical model for the unsteady shear-stress driven flow of a rivulet of Newtonian fluid and non-Newtonian power-law fluids on an inclined plane is formulated and analysed. The cross-sectional profile of the symmetrical rivulet with a free parameter in the ordinary differential equation is determined. It is shown that the height, the semi-width, the area and the Volume flux of rivulet depend on that equation. Further analysis shows that the physically realisable rivulet solution is only found in the single-humped cross-sectional profile. The rivulet of a fixed nose at the origin travels down the inclined plane and becomes narrower and thinner with time, while maintaining its cross-sectional shape. © 2024 Author(s).
|
|---|