THE DUHEM-HADAMARD HYPOTHESIS IN THERMOFLUID DYNAMICS

The Duhem-Hadamard hypothesis (DHH) states that in a fluid flow the sa me equation relates the pressure, the mass density,and the temperature as in equilibrium. The entire theory of bodies concerning flow proces ses in engineering science and practice rests upon it. Our recent work on fundamentals of non-equilibrium phenomena suggests that the hypoth esis are only approximate in some sense, but its mathematical formulat ion does not make clear what is being approximated. To get a prelimina ry clarification, the paper deals with two items: first, a theoretical basis is worked out to yield appropriate presuppositions for an effic ient experimental program and, second, provisional experimental data a re established by a new and precise set-up. Our theoretical examinatio ns admit to derive definite distinguishing Features of both non-equili brium and equilibrium processes. The latter appear as a limiting case of the former and are identified with the hypothetical fluid state at rest. Only for this special state the thermal equation of state is rep resentative of thermo;dynamic equilibrium. Yet, there is a second kind of equilibrium: the kinetic equilibrium defined for reversible flows. All theoretical considerations lead us to the conclusion that the DHH can only be justified for kinetic equilibria. The first phase of our research program allowed to learn that our high-precision measurement devices need to be improved in order to decide, whether this special k ind of reversible flow exists as a real limiting case. Unlike this, ou r experiments prove that non-equilibrium states induced by the motions of the fluid cannot be described by the DHH. (C) 1998 Published by El sevier Science Ltd. All rights reserved.