Non-Newtonian pseudoplastic fluids: Analytical results and exact solutions

Abstract

A one layer model of laminar non-Newtonian fluids (Ostwald–de Waele 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 − 2 n ) 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 γ , 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 γ = 0 (impermeable surface). For γ ≠ 0 (permeable surface) we obtain a unique pseudosimilarity solution for any 0 ≠ γ ≥ − ( ( n + 1 ) / 3 n ( 1 − 2 n ) ) 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.