Linear Irreversible Thermodynamics

The conservation laws for (partial) mass, momentum and (total, internal, kinetic) energy contain non-convective fluxes as well as chemical reaction rates. These quantities depend on the material and the nonequilibrium flow state of the system through constitutive equations that must be specified based on rational arguments. In this chapter we employ the assumption of Local Thermodynamic Equilibrium (LTE) to construct the second law of thermodynamics—the balance law for entropy—accompanying the conservation laws. The constitutive equations are obtained from the requirement that the local entropy generation rate must be non-negative, and vanishes in equilibrium.