Similarity Solution for an Unsteady Dry Patch in a Shear-Stress-Driven Thin Film of Non-Newtonian Power-Law Fluid

摘要

In this study, the lubrication approximation is used to derive the governing equations for the unsteady flow of non-Newtonian power-law fluid around a symmetric slender dry patch on an inclined plane. The flow is driven by a constant shear stress at the free surface, and we assume that surface-tension effect is neglected. The governing partial differential equation is transformed into the ordinary differential equation using a unique travelling-wave similarity transformation. We obtain a one-parameter family of solutions parameterised by the non-dimensional velocity of the dry patch, . The similarity solution is independent of the power-law index, N and it predicts that the dry patch has a parabolic shape.