Extended hydrodynamics from Enskog's equation for a two-dimensional system general formalism

Balance equations are derived from Enskog’s kinetic equation for a two-dimensional system of hard disks using Grad’s moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional fluids. The set of independent hydrodynamic fields in the present formulations are: density, velocity, temperature {\em and also}–following Grad’s original idea–the symmetric and traceless pressure tensor $p_{ij}$ and the heat flux vector ${\mathbf{q}}^k$. An approximation scheme similar in spirit to one made by Grad in his original work is made. Once the hydrodynamics is derived it is used to discuss the nature of a simple one-dimensional heat conduction problem. It is shown that, not too far from equilibrium, the nonequilibrium pressure in this case only depends on the density, temperature and heat flux vector.