M. Pakdemirli, SIMILARITY ANALYSIS OF BOUNDARY-LAYER EQUATIONS OF A CLASS OF NON-NEWTONIAN FLUIDS, International journal of non-linear mechanics, 29(2), 1994, pp. 187-196
A similarity analysis of three-dimensional boundary layer equations of
a class of non-Newtonian fluids in which the stress is an arbitrary f
unction of rates of strain is made. It is shown that under scaling tra
nsformation, for an arbitrary stress function, only 90-degrees of wedg
e flow leads to similarity solutions, whereas for a specific more rest
ricted form, similarity solutions exist for arbitrary wedge angles. In
the case of spiral group transformation, no similarity solutions exis
t if we force the stress function to remain arbitrary after the transf
ormation, whereas for a specific more restricted form, similarity solu
tions exist for arbitrary wedge angles. For both transformations, simi
larity equations for power-law and Newtonian fluids are presented as s
pecial cases of the analysis. Finally the conditions for invariance an
d the form of the stress function for a two-dimensional case are also
presented.