  We aim at studying gasodynamic vortex cooling in an analytically solvable,
thermodynamically consistent model that can explain limitations on the cooling
efficiency. To this end, we study a angular plus radial flow between two
(co-axial) rotating permeable cylinders. Full account is taken of
compressibility, viscosity and heat conductivity. For a weak inward radial flow
the model qualitatively describes the vortex cooling effect|both in terms of
temperature and of decrease of the stagnation enthalpy|seen in short uniflow
vortex (Ranque) tubes. The cooling does not result from external work, and its
efficiency is defined as the ratio of the lowest temperature reached
adiabatically (for the given pressure gradient) to the actually reached lowest
temperature. We show that for the vortex cooling the efficiency is strictly
smaller than 1, but in another configuration with an outward radial flow, we
found that the efficiency can be larger than 1. This is related to both the
geometry and the finite heat conductivity.
