Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls

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Abstract

The self-similar two-dimensional steady boundary-layer flow induced by a permeable surface stretching with velocity Uw(x)=A·xm in a quiescent fluid in the presence of suction or injection with velocity Vw(x)=a·x(m−1)/2 is considered for A>0 and m>−1. The exact analytic solutions of this problem are given for m=−1/3 and m=−1/2 and the mechanical characteristics of the corresponding flows are discussed in detail. Boundary layers of the same thickness corresponding to different lateral mass fluxes are described. It is shown that to the smallest entrainment velocity, there corresponds a vanishing skin friction, i.e. a `dragless motion' of the fluid. The exact results are also compared with the results of the analytical approximations reported recently by other authors (in a physically different but mathematically identical context) in this journal.

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