A note on the temperature dependence of the normal stress moduli

Abstract

In this analysis we establish necessary and sufficient conditions which the normal stress modulus [alpha]1([theta]) and its derivative d[alpha]1([theta])/d[theta] ought to satisfy if a homogeneous incompressible second grade fluid is to meet the requirement that the specific internal energy of the fluid be a minimum when the fluid is locally at rest. We also require that all arbitrary motions of the fluid meet the Clausius-Duhem inequality. It is found that requiring that the specific internal energy of the fluid be a minimum when the fluid is locally at rest is not equivalent to a similar requirement on the specific Helmholtz free energy.