Some two dimensional exact solutions have been obtained describing nonsteady flows of second order incompressible fluids. The results are expressed in terms of a non-dimensional parameter which depends on the non-Newtonian coefficient and the frequency of excitation of the external disturbance. It is noticed that for a cri~ical vahe of K (= Kc), the flow properties are identical with those in the Newtonian case. ยง 1. Introduction. Noll a) defined a simple material as a substance for which the stress can be determined with the entire knowledge of the history of the strain. This is called a simple/luid, if it has the property that all local states, with the same mass density, are intrinsically equivalent in response, with all observable differences in response being due to definite differences in history. For any given history g(s), a retarded history ga(s) can be defined as ca(s) = ยซ(es); 0 < s < o~, 0 < ~ ~< 1 (1.1)
ยซ being termed as a retardation factor. Assuming that the stress is more sensitive to recent deformation than to deformations at distant past, Coleman and Noll 1) proved that the theory of simple fluids yields the theory of perfect fluids as ยซ -+ 0 and that *) Before communicating this note, it has been noticed from a recent paper: "Nonsteady helieal flows of seeond-order flows" by l-I. Markovitz and ]3. D. Coleman Cf : Physics of Fluids 7 (1964) 83g that Tr ue s dell eonsidered some problems involving standing waves in second order fIuids (unpublished). The results of TruesdelI are, however, not known to the present author.