  The Boltzmann equation for inelastic and rough hard spheres is considered as
a model of a dilute granular gas. In this model, the collisions are
characterized by constant coefficients of normal and tangential restitution and
hence the translational and rotational degrees of freedom are coupled. A normal
solution to the Boltzmann equation is obtained by means of the Chapman-Enskog
method for states near the homogeneous cooling state. The analysis is carried
out to first order in the spatial gradients of the number density, the flow
velocity, and the granular temperature. The constitutive equations for the
momentum and heat fluxes and for the cooling rate are derived and the
associated transport coefficients are expressed in terms of the solutions of
linear integral equations. For practical purposes, a first Sonine approximation
is used to obtain explicit expressions of the transport coefficients as
nonlinear functions of both coefficients of restitution and the moment of
inertia. Known results for purely smooth inelastic spheres and perfectly
elastic and rough spheres are recovered in the appropriate limits.
