Free-molecule tube flow and adiabatic wall temperatures

The processes of mass and convective-energy transport in free-molecule flow are shown to bear useful similarities with the process of energy transport by thermal radiation. These similarities have been applied as a basis for deriving the mass and energy transfer characteristics for free-molecule flow in a circular tube. The net mass flow through tubes of various length-diameter ratios has been calculated as a function of the pressures and temperatures at the inlet and exit of the tube. A throughflow may occur even if the inlet and exit pressures are the same, provided that a temperature difference exists. For a length-diameter ratio in excess of 45, a fully developed mass flow relation applies. The distribution of the adiabatic wall temperature along the tube length has also been determined as a function of system pressures and temperatures and of the tube dimensions. Rather large variations of adiabatic wall temperature may occur for long tubes. The throughflow of energy shows characteristics similar to the throughflow of mass.