Nonequilibrium ensemble derivation of hydrodynamic heat transport and higher-order generalizations

Thermal transport in classical fluids is analyzed through higher-order generalized hydrodynamics (or mesoscopic hydrothermodynamics) depending on the evolution of the energy density and its fluxes of all orders. It is derived by a kinetic theory based on the nonequilibrium statistical ensemble formalism. A general system of coupled evolution equations is derived. Maxwell times, which are of significance to determine the character of the motion, are derived. They also have an important role in the choice of the contraction of description (limitation in the number of fluxes to be retained) in the studies on hydrodynamic motions. In a description of order 1, an analysis of the technological process of thermal prototyping is presented.