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We describe a special class of steady Couette flows in dilute granular gasesadmitting a non-Newtonian hydrodynamic description for strong dissipation. Theclass occurs when viscous heating exactly balances inelastic cooling, resultingin a uniform heat flux. It includes the Fourier flow of ordinary gases and thesimple or uniform shear flow (USF) of granular gases as special cases. Therheological functions have the same values as in the USF and generalizedthermal conductivity coefficients can be identified. These points are confirmedby molecular dynamics simulations, Monte Carlo simulations of the Boltzmannequation, and analytical results from Grad's 13-moment method.

Non-Newtonian granular hydrodynamics. What do the inelastic simple shear flow and the elastic Fourier flow have in common?