On sheet-driven motion of power-law fluids

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)=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 0.1n2.0 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.