This paper considers the flow of viscous incompressible fluids in an annular channel, on the inner and outer surfaces of which intensive heat exchange conditions are set, mathematical formulation of which is reduced to boundary  conditions of the first kind. Differenttemperature dependencies of liquid viscosity are considered: monotonic (liquid viscosity decreases monotonously as the temperature rises) and anomalous (liquid viscosity depends on the  temperature in a non-monotonic way). Mathematical model comprises continuity, Navier- Stokes and energy conservation equations written in cylindrical coordinate system with axial symmetry considered in dimensionless form. The  equations of the mathematical model were solved numerically using the method of control volume. Because of numerical simulation, velocity diagrams in various sections of the annular channel, as well as distributions of temperature  and viscosity fields in the flow area, have been plotted. The influence of geometric parameters of the annular channel, heat exchange conditions on its walls and rheological parameters of the fluid on the flow pattern has been  determined. It is shown that in a liquid with a non-monotone dependence of viscosity on temperature, the hydrodynamic parameters of the flow significantly depend on the location of the high-viscosity flow region (the “viscous barrier”).