The flow of plasma into a perfectly absorbing wall, primarily in the sheath and presheath regions, is investigated. Fluidlike moment equations are derived from kinetic theory to include the improved parallel viscosity and heat flux for a transition region between the collisional presheath and the collisionless sheath of the plasma. Both the electron and ion distribution functions are obtained. The ion viscous force, which has usually been considered to be a small term, is deduced from the distribution function, and it is found to be comparable to the electric field force everywhere. The treatment removes the singularity between the presheath and sheath regions in the ion moment equations. One of the results is that, because of the thermal conduction effects in the sheath region, the total heat flux at the wall is larger (∼30%) than in previous work.