The similarity equations that arise when there is a power-law outer flow, characterized by the parameter β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document}, over a surface moving with the same power-law speed, described by the dimensionless parameter λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document}, are considered. The critical values λc\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _c$$\end{document} of λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document} are calculated in terms of β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document}, except in a range 0.139≲β≲0.5\documentclass[12pt]{minimal}
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\begin{document}$$0.139 \lesssim \beta \lesssim 0.5$$\end{document} where there are no critical points. The behaviour of the solution with λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document} for representative values of β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document} is examined, including cases where there are no critical points and one or two critical points leading to two and three solution branches. The asymptotic behaviour for large λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document} is derived. For -2<β<-1\documentclass[12pt]{minimal}
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\begin{document}$$-2<\beta <-1$$\end{document}, the solution proceeds to large negative values of λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document} with this asymptotic limit derived. Aiding flow, λ>0\documentclass[12pt]{minimal}
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\begin{document}$$\lambda >0$$\end{document}, shows the existence of additional critical points, with a range -2.6583<β<-2\documentclass[12pt]{minimal}
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\begin{document}$$-2.6583<\beta <-2$$\end{document} over which λc\documentclass[12pt]{minimal}
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\begin{document}$$\lambda _c$$\end{document} takes all values both positive and negative. Relatively weak, λ=-0.5\documentclass[12pt]{minimal}
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\begin{document}$$\lambda =-0.5$$\end{document}, and stronger, λ=-5.0\documentclass[12pt]{minimal}
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\begin{document}$$\lambda =-5.0$$\end{document}, cases of opposing are treated. The weak case shows two disjoint sections of the solution. For the larger value of |λ|\documentclass[12pt]{minimal}
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\begin{document}$$|\lambda |$$\end{document}, one section of the solution in which f′′(0)\documentclass[12pt]{minimal}
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\begin{document}$$f''(0)$$\end{document} decreases monotonically as β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document} is increased and another section where there is a critical point with two solution branches is seen. In all the cases considered, the solution became singular as β→-2\documentclass[12pt]{minimal}
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\begin{document}$$\beta \rightarrow -2$$\end{document}, this limit being discussed.
