ON STEADY MOTIONS IN THERMODYNAMICS

We herein refine the strategy first formalized by Coleman and Noll for deducing constitutive restrictions from the Clausius-Duhem inequality . Specifically, we establish a key lemma that for certain materials al lows the Coleman-Noll procedure to be carried out within just the clas s of steady motions. By so shrinking the size of the process class nee ded to employ the Coleman-Noll procedure, our lemma simultaneously enl arges the class of real materials that we know must be mindful of cert ain of the constitutive restrictions that descend from the principles of thermodynamics. In particular, our lemma allows a thermodynamic ana lysis, using just steady motions, of fluids of differential type-a con stitutive class that the rheological community frequently lays down as governing material response in steady motions, although it is ambival ent about the use of such forms in more general motions. Thermodynamic s is thus shown to deliver significant constitutive restrictions witho ut anything being postulated for material response on nonsteady motion s. (C) 1997 Elsevier Science Ltd.