  A kinetic theory for moderately dense gases of inelastic and rough spherical
molecules is developed from the Enskog equation where a macroscopic state is
characterized by 29 scalar fields which correspond to the moments of the
distribution function: mass density, hydrodynamic velocity, pressure tensor,
absolute temperature, translational and rotational heat fluxes, hydrodynamic
angular velocity and angular velocity flux. The balance equations for the 29
scalar fields are obtained from a transfer equation derived from the Enskog
equation where the kinetic and potential parts of the new moments of the
distribution function and production terms are calculated from Grad's
distribution function for the basic fields. The transition from the 29 field
theory to an eight field theory -- with mass density, hydrodynamic velocity,
absolute temperature and hydrodynamic angular velocity -- leads to the
determination of the transport coefficients of the Navier-Stokes and Fourier
laws. The transport coefficients are functions of the normal and tangential
restitution coefficients and of the local equilibrium radial distribution
function. The transport coefficients in the limiting case of elastic rough
spheres is also determined.
