Multipolar viscous fluids. (English) Zbl 0732.76003

In this paper a thermodynamic theory of constitutive equations of multipolar viscous fluids is derived. The postulated constitutive equations express the free energy, entropy, heat flux vector, and the multipolar stress tensors as functions of density and its gradients up to a fixed order, the gradients of velocity up to a fixed order, the temperature, and the gradient of temperature. The general restrictions which the principle of material frame-indifference and the Clausius-Duhem inequality place on the constitutive functions of the fluid are deduced. Explicit forms of the viscous stresses are obtained for linear viscous fluids. As in the classical case, the Clausius-Duhem inequality gives the nonnegativeness of the viscous work which, in the strengthened form, plays a crucial role in the existence theory.


76A02 Foundations of fluid mechanics
80A10 Classical and relativistic thermodynamics
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