  We study the non-equilibrium steady-states of a one-dimensional ($1D1V$)
fluid in a finite space region of length $L$. Particles interact among
themselves by multi-particle collisions and are in contact with two
thermal-wall heat reservoirs, located at the boundaries of the region. After an
initial ballistic regime, we find a crossover from a normal (kinetic) transport
regime to an anomalous (hydrodynamic) one, above a characteristic size $L_*$.
We argue that $L_*$ is proportional to the cube of the collision time among
particles. Motivated by the physics of emissive divertors in fusion plasma, we
consider the more general case of thermal walls injecting particles with given
average (non-thermal) velocity. For fast and relatively cold particles, short
systems fail to establish local equilibrium and display non-Maxwellian
distributions of velocities.
