Temperature profile for Poiseuille flow

For planar Poiseuille flow of an atomic fluid in the weak-flow regime, we find that the classical Navier-Stokes prediction of a quartic temperature profile is incorrect. Our results, which confirm a prediction made by Baranyai, Evans, and Daivis (BED) [Phys. Rev. A 46, 7593 (1992)], indicate that near the center of the channel the temperature profile is quadratic. When the temperature profile is fitted to the theoretical predictions of BED we obtain estimates of the thermal conductivity that are in excellent agreement with accurate independent estimates of this transport coefficient. If the presence of the quadratic component of the temperature profile is ignored, the derived value of the thermal conductivity is in error by some 50%.