Calculation of the Ranque effect in the vortex tube

The theoretical model allowing to calculate correctly the observed temperature separation along the tube radius is presented here. The model is based on the original analytical solution of the general problem and calculation of hydrodynamics of complex spatial vortex flow in a tube. The model allows to derive three components of velocity analytically using the ideal incompressible liquid approximation and to obtain the complex spatial flow structure with helical vortex in a tube. Then the known hydrodynamic field of velocity is introduced into the equation of convective heat transfer. The solution of the obtained equation, in which only the convective transfer due to complex topology of hydrodynamic field is taken into account, permits to obtain the temperature field distribution. The region of decreased temperature is in the center, and that of increased temperature is placed on the periphery. Counter flow of liquid in the center is observed depending on the step of helix. The obtained solution for the velocity field allows to calculate the phenomenon of the vortex reverse effect too.