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Falkner-Skan boundary layer flow of a power-law fluid past a stretching wedge. (English) Zbl 1416.76011
Summary: The steady two-dimensional laminar boundary layer flow of a power-law fluid past a permeable stretching wedge beneath a variable free stream is studied in this paper. Using appropriate similarity variables, the governing equations are reduced to a single third-order highly nonlinear ordinary differential equation in the dimensionless stream function, which is solved numerically using the Runge-Kutta scheme coupled with a conventional shooting procedure. The flow is governed by the wedge velocity parameter \(\lambda \), the transpiration parameter \(f_{0}\), the fluid power-law index \(n\), and the computed wall shear stress is \(f^{\prime\prime}(0)\). It is found that dual solutions exist for each value of \(f_{0}, m\) and \(n\) considered in \(\lambda - f^{\prime\prime}(0)\) parameter space. A stability analysis for this self-similar flow reveals that for each value of \(f_{0}, m\) and \(n\), lower solution branches are unstable while upper solution branches are stable. Very good agreements are found between the results of the present paper and that of P. D. Weidman et al. [Int. J. Eng. Sci. 44, No. 11–12, 730–737 (2006; Zbl 1213.76064)] for \(n = 1\) (Newtonian fluid) and \(m = 0\) (Blasius problem [H. Blasius, Schlömilch’s Z. Math. Phys. 56, 1–37 (1908; JFM 39.0803.02)]).

MSC:
76A05 Non-Newtonian fluids
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76M20 Finite difference methods applied to problems in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
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