Heat flux of a granular gas with homogeneous temperature

A steady state of a granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position–dependent force or by enclosing the grains inside a curved two–dimensional silo. At a macroscopic level, the state is identified with one solution to the inelastic Navier–Stokes equations, due to the coupling between the heat flux induced by the density gradient and the external force. On the contrary, at the mesoscopic level, by exactly solving a BGK model or the inelastic Boltzmann equation in an approximate way, a one–parametric family of solutions is found. Molecular dynamics simulations of the system in the quasi–elastic limit are in agreement with the theoretical results.