Derivation of constitutive data for flowing fluids from comparable data for quiescent fluids

Abstract

The principles of linear irreversible thermodynamics are used to show that near-equilibrium linear constitutive equations governing the diffuse fluxes through fluids of momentum, energy, and other extensive properties, and valid for the case of general unsteady flows, can be derived by inspection solely from knowledge of their steady-state quiescent-fluid counterparts. This includes predictions not only of the general forms of these flux-force constitutive equations but also of the values of the phenomenological coefficients appearing therein. To supplement these diffuse flux data so as to effect closure of the fundamental equations of hydrodynamics, constitutive knowledge is also required of the relation between the fluid’s specific momentum density (momentum “velocity”) mˆ appearing in the inertial term of the momentum equation, and its mass velocity vm appearing in the continuity equation. Towards this end, and with jv the diffuse flux of volume, a plausible argument is advanced favoring the view that mˆ=vm+jv over that of Euler’s currently accepted (albeit implicit) hypothesis that mˆ=vm, with the two possibilities currently a matter of contention.