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.

开发了流体的完全二阶连续介质理论。使用传统的质量、线性动量、能量和熵的平衡方程。假定本构方程取决于密度、温度和速度，以及它们的二阶导数。等存在性原理与 Coleman-Noll 过程一起使用，以利用第二定律推导出对本构方程的限制。不假定熵通量等于温度范围内的热通量。我们获得了直到二次非线性的所有本构量的明确结果，以满足 Clausius-Duhem 不等式。我们的结果被证明是一致的，但比其他已发表的结果更普遍。