A Phenomenological Gradient Approach to Generalized Constitutive Equations for Isotropic Fluids

Abstract

An extension of the linear irreversible thermodynamics is proposed through the inclusion of the first gradients of velocity and of the classical local state parameters as additional independent variables in the fundamental energy state equation of a fluid system. We show that consistency of this hypothesis with the energy balance equation leads to generalized nonlinear constitutive equations, which we discuss in terms of an isotropic non-Newtonian viscous fluid.