The interaction between a plasma and a solid surface is studied in a (1D-1V) kinetic framework using a localized particle and convective energy source. Matching the quasineutral plasma region and sheath horizon is addressed in the fluid framework with a zero heat flux closure. It highlights non-polytropic nature of the physics of parallel transport. Shortfalls of this approach compared to a reference kinetic simulation, highlighting the importance of the heat flux, leads to addressing the sound velocity, non-collisional closure and higher moment closure. No gain in the predictive capability is obtained. The kinetic constraint at the sheath horizon is discussed and modified to account for conditions that are actually met in simulations, namely quasineutrality with a small but finite charge density. Analyzing the distribution functions shows that collisional transfer is mandatory to achieve steady-state self-organization on the open field lines.