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The entrainment theorem for wall driven boundary layer

Boundary layer ﬂows driven by permeable plane surfaces, stretching with power–law velocities are considered in the presence of an applied lateral mass ﬂux. The relationship between the wall shear stress and the entrainment velocity (the transversal velocity at the outer edge of the boundary layer) as a function of the mass transfer parameter f w is examined analytically by using the Merkin transformation method. It is shown that at the value of f w where the wall shear stress vanishes, the entrainment velocity reaches a minimum or maximum value. This relationship between two characteristic quantities at the outer and inner edge of the boundary layer, respectively, is referred to as entrainment theorem . Its physical content is analyzed in the paper in some detail.