Non-Newtonian pseudoplastic fluids: Analytical results and exact solutions

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 x1/(1−2n)x1/(1−2n) and x−1, respectively, where n   is the power-law index which is taken in the interval (0,12). It is shown that the boundary-layer equations display both similarity and pseudosimilarity reductions according to a parameter γγ, 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=0γ=0 (impermeable surface). For γ≠0γ≠0 (permeable surface) we obtain a unique pseudosimilarity solution for any 0≠γ≥−((n+1)/3n(1−2n))n/(n+1)0≠γ≥−((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.

► In this study we examine a class of non-Newtonian pseudoplastic fluids. ► The power-law index is taken in the interval (0,1/2). ► Exact similarity solutions are obtained in a closed form. ► New explicit solutions are also obtained using the translation invariance method.