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.