Similarity flow solutions of a non-Newtonian power-law fluid. (English) Zbl 1285.76004

Summary: We present a mathematical analysis for a steady-state laminar boundary layer flow, governed by the Ostwald-de Waele power-law model of an incompressible non-Newtonian fluid past a semi-infinite power-law stretched flat plate with uniform free stream velocity. A generalization of the usual Blasius similarity transformation is used to find similarity solutions. Under appropriate assumptions, partial differential equations are transformed into an autonomous third-order nonlinear degenerate ordinary differential equation with boundary conditions. Using a shooting method, we establish the existence of an infinite number of global unbounded solutions. The asymptotic behavior is also discussed. Some properties of those solutions depend on the viscosity power-law index.


76A05 Non-Newtonian fluids
34B40 Boundary value problems on infinite intervals for ordinary differential equations
Full Text: arXiv