Second-order constitutive theory of fluids

A fully second-order continuum theory of fluids is developed. The conventional balance equations of mass, linear momentum, energy and entropy are used. Constitutive equations are assumed to depend on density, temperature and velocity, and their derivatives up to second order. The principle of equipresence is used along with the Coleman–Noll procedure to derive restrictions on the constitutive equations by utilizing the second law. The entropy flux is not assumed to be equal to the heat flux over the temperature. We obtain explicit results for all constitutive quantities up to quadratic nonlinearity so as to satisfy the Clausius–Duhem inequality. Our results are shown to be consistent but more general than other published results.