Note on semi‐analytical nonstationary solution for the rivulet flows of non‐Newtonian fluids

Abstract

We have presented in this analytical research the revisiting of approach for mathematical modeling the rivulet flows on inclined surface in terms of viscous‐plastic theory of two‐dimensional movements in a frame of (x, y)‐plane in Cartesian coordinates. A semi‐analytical solution has been obtained here for nonstationary creeping approximation of plane‐parallel flow slowly moving on inclined surface. The main motivation of the current development is that each additional enhancement of knowledge in regard to this phenomenon should obviously improve the accuracy of calculations for possible applications in technological or engineering areas of fluid dynamics researches. Even in such simple formulation, equations of motion that govern the dynamics of rivulet flows of non‐Newtonian fluids are hard to be solved analytically. Nevertheless, we have succeeded in obtaining analytical expressions for the components of velocity in {Ox, Oy}‐directions of motion for slowly moving the advancing front of rivulet flow (where Ox‐axis coincides to the initial main direction of slowly moving rivulet flow). Restrictions to the form of flow (stemming from the continuity equation) have been used accordingly.