On the Mechanical Inadmissibility and Thermodynamic Admissibility According to the Clausius-duhem Inequality of the Unbounded Shear Flow of a Second-order Fluid with Negative Stress Power*

Recently, Rajagopal [1] has considered an unsteady shearing flow of the incompressible second-order fluid with the constitutive equation for the extra stress S given by S = juAj 4axA2 + «2^i(1) In (1), ju, aj, a2 are constants, with jn > 0; \1 and A2 are the first two Rivlin-Ericksen tensors [2]. Rajagopal [1] showed that the time-dependent plane flow x = u(y,t), y = 0, in {x, y, t) e (-oo, oo) X (0, oo) X (0, oo), (2) satisfied the equations of motion, including inertia but excluding body forces, for the second-order fluid described by (1) above when u(y,t) = Ue'mycos(w/ ny). (3) In (2), U (> 0), w (> 0), m and n are constants; moreover, if p is the density of the fluid, then