  We describe a special class of steady Couette flows in dilute granular gases
admitting a non-Newtonian hydrodynamic description for strong dissipation. The
class occurs when viscous heating exactly balances inelastic cooling, resulting
in a uniform heat flux. It includes the Fourier flow of ordinary gases and the
simple or uniform shear flow (USF) of granular gases as special cases. The
rheological functions have the same values as in the USF and generalized
thermal conductivity coefficients can be identified. These points are confirmed
by molecular dynamics simulations, Monte Carlo simulations of the Boltzmann
equation, and analytical results from Grad's 13-moment method.
