On sheet-driven motion of power-law fluids

Abstract

A rigorous analysis of non-Newtonian boundary layer flow of power-law fluids over a stretching sheet is presented. First, a systematic framework for treatment of sheet velocities of the form $U(x)={\mathit{Cx}}^m$ is provided. By means of an exact similarity transformation, the non-linear boundary layer momentum equation transforms into an ordinary differential equation with m and the power-law index n as the only parameters. Earlier investigations of a continuously moving surface $(m=0)$ and a linearly stretched sheet $(m=1)$ are recovered as special cases. For the particular parameter value $m=1$, i.e. linear stretching, numerical solutions covering the parameter range $0.1⩽n⩽2.0$ are presented. Particular attention is paid to the most shear-thinning fluids, which exhibit a challenging two-layer structure. Contrary to earlier observations which showed a monotonic decrease of the sheet velocity gradient $-f^{″}(0)$ with n, the present results exhibit a local minimum of $-f^{″}(0)$ close to $n=1.77$. Finally, a series expansion in $(n-1)$ is proved to give good estimates of $-f^{″}(0)$ both for shear-thinning and shear-thickening fluids.