In this paper, the flow of an anomalously thermo - viscous incompressible fluid in an annular channel, on the inner and outer surfaces of which convective heat transfer to the environment according to the Newton-Richman law, is considered. The viscosity of the fluid depends on the temperature in a non-monotone way. The mathematical model includes the continuity equation, Navier-Stokes equation, and temperature equation written in a cylindrical coordinate system with axial symmetry. As a result of numerical modeling, velocity diagrams in different cross sections of the annular channel and distributions of temperature and viscosity fields have been got. The influence of heat exchange conditions on the walls and rheological parameters of the fluid on the flow character are established. It is shown that a liquid with a non-monotone dependence of viscosity the hydrodynamic parameters of the flow depend on the location of the flow area with increased viscosity—the “viscous barrier”.