Heat pump model for Ranque–Hilsch vortex tubes

We describe a quantitative model for heat separation in a fluid due to motion along a pressure gradient. The physical model involved is relevant to one explanation for the temperature separation in a vortex tube. This effect has a point of saturation in which the fluid's temperature and pressure are related at its boundaries by an adiabatic law. Vortex tube models sometimes assume that this saturation is achieved in physical devices. We conclude that this is likely to be a safe assumption much of the time, but we describe circumstances in which saturation might not be achieved. We propose a test of our model of temperature separation.