Internal Variables as a Tool for Extending Navier-Stokes Equations

Abstract The formalism of the internal variable theory is applied to extend Navier-Stokes equations. The internal variable theory provides a thermodynamically consistent derivation of constitutive relations and equations of motion without a priori specifying the nature of internal variables. Both single and dual internal variables cases are thoroughly examined. The similarities and differences of the approaches are emphasized. In the single internal variable framework, the elimination of the internal variable results in Maxwell-type constitutive relations and hyperbolic equations of motion. The dual internal variable technique enables us to create even more sophisticated fluid flow models with coupled equations for fluid motion and internal variable evolution.