The Duhem—Hadamard hypothesis in thermofluiddynamics

• Published in: International journal of non-linear mechanics 1998-11, Vol.33 (6), p.993-1012
• Main Authors: Neumaier, M., Lauster, M., Lippig, V., Waibel, R., Straub, D.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Thermodynamics
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/S0020-7462(97)00063-2

The Duhem–Hadamard hypothesis (DHH) states that in a fluid flow the same equation relates the pressure, the mass density, and the temperature as in equilibrium. The entire theory of bodies concerning flow processes in engineering science and practice rests upon it. Our recent work on fundamentals of non-equilibrium phenomena suggests that the hypothesis are only approximate in some sense, but its mathematical formulation does not make clear what is being approximated. To get a preliminary clarification, the paper deals with two items: first, a theoretical basis is worked out to yield appropriate presuppositions for an efficient experimental program and, second, provisional experimental data are established by a new and precise set-up. Our theoretical examinations admit to derive definite distinguishing features of both non-equilibrium 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 representative of thermodynamic 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 kind of reversible flow exists as a real limiting case. Unlike this, our experiments prove that non-equilibrium states induced by the motions of the fluid cannot be described by the DHH.