Some viscometric flows of incompressible thermoviscous fluids

Abstract

Recently Coleman and Mizel, and Koh and Eringen have proposed sets of constitutive equations for ideal materials called thermoviscous fluids. Here we study one set of equations from each pair of authors. The predictions of these two sets of constitutive equations for some viscometric flows are compared and it is shown that in the absence of body forces and heat sources these flows exist for the Coleman-Mizel fluid, but not for the Koh-Eringen fluid. The difference between the two sets of constitutive equations arises because the Coleman-Mizel stress equation is invariant under improper co-ordinate transformations and the Koh-Eringen one is invariant under proper orthogonal transformations. Hence an experimental basis is suggested here for determining if a stress constitutive equation should be invariant under improper and proper transformations or only under proper ones.