Non-Newtonian pseudoplastic fluids: Analytical results and exact solutions

A one layer model of laminar non-Newtonian fluids (Ostwald-de Wade model) past a semi-infinite flat plate is revisited. The stretching and the suction/injection velocities are assumed to be proportional to x(1/(1-2n)) and x(-1), respectively, where n is the power-law index which is taken in the interval (0, 1/2). It is shown that the boundary-layer equations display both similarity and pseudosimilarity reductions according to a parameter gamma, which can be identified as suction/injection velocity. Interestingly, it is found that there is a unique similarity solution, which is given in a closed form, if and only if gamma = 0 (impermeable surface). For gamma not equal 0 (permeable surface) we obtain a unique pseudosimilarity solution for any 0 not equal gamma >= -((n+1)/3n(1-2n))(n/(n+1)). Moreover, we explicitly show that any pseudosimilarity solution exhibits similarity behavior and it is, in fact, similarity solution to a modified boundary-layer problem for an impermeable surface. In addition, the exact similarity solution of the original boundary-layer problem is used, via suitable transverse translations, to construct new explicit solutions describing boundary-layer flows induced by permeable surfaces. (C) 2011 Elsevier Ltd. All rights reserved.