  In order to improve the presently used ad hoc flux limiter treatment of
parallel heat flux transport in edge plasma fluid codes we consider here a
generalized version of the Fourier law implementing a non-local kernel for the
heat flux computation. The Bohm boundary condition at the wall is recovered
introducing a volumetric loss term representing the contribution of
suprathermal particles to the energy out flux. As expected, this contribution
is negligible in the strongly collisional regime while it becomes more and more
dominant for marginally and low collisional regimes. In the second part of the
paper, we consider a kinetic approach where collisions are considered using the
Multi-Particle-Collision (MPC) algorithm. Kinetic simulation results at medium
and low collisionality are also reported.
