A remark on similarity analysis of boundary layer equations of a class of non-Newtonian fluids

• Similarity analysis is made of the three-dimensional steady incompressible laminar boundary layer flow of a general class of non-Newtonian fluids.
• From the present analysis, it is observed that for the non-Newtonian fluids of any model similarity solutions exist only for the flow past a 90° wedge.
• It is also worth to observe that for the boundary layer flow of all non-Newtonian fluids past any body shape whose shearing stress is either implicit or composite function of the rate of strain only non-similar solutions exist.
• The present analysis illustrates similarity and non-similarity among the different models of non-Newtonian fluids.

A similarity analysis of three-dimensional boundary layer equations of a class of non-Newtonian fluid in which the stress, an arbitrary function of rates of strain, is studied. It is shown that under any group of transformation, for an arbitrary stress function, not all non-Newtonian fluids possess a similarity solution for the flow past a wedge inclined at arbitrary angle except Ostwald-de-Waele power-law fluid. Further it is observed, for non-Newtonian fluids of any model only 90°90° of wedge flow leads to similarity solutions. Our results contain a correction to some flaws in Pakdemirli׳s [14] (1994) paper on similarity analysis of boundary layer equations of a class of non-Newtonian fluids.