An openFOAM computational fluid dynamic simulation model was developed for the description of local interaction of hydrodynamics and Joule heating in annular electrochromatography. A local decline of electrical conductivity of the background eluent is caused by an electrokinetic migration of ions resulting in higher Joule heat generation. The model equations consider the Navier-Stokes equation for incompressible fluids, the energy equation for stationary temperature fields, and the mass transfer equation for the electrokinetic flow. The simulations were embedded in commercial ANSYS Fluent software and in open-source environment openFOAM. The annular gap (1mm width) contained an inorganic C8 reverse-phase monolith as stationary phase prepared by an in situ sol-gel process. The process temperature generated by Joule heating was determined by thermal camera system. The local hydrodynamics in the prototype was detected by a gravimetric contact-free measurement method and experimental and simulated values matched quite well.