Two-dimensional numerical calculations in cylindrical shell geometry have been carried out to investigate the effect of the temperature-dependent viscosity on the pattern and the characteristic parameters of the thermal convection occurring in the Earth's mantle. Systematic model runs established that the viscosity decreasing with the temperature is reduced around the hot core-mantle boundary (CMB) which facilitates 'the heat transport' from 'the core to the mantle'. On the other hand, the viscosity increases near the cold surface which hinders the heat outcome and results in higher mantle temperature and lower surface velocity. A power law relation was revealed between the strength of the temperature-dependence and the observed parameters, such as the velocity, surface mobility, heat flow, average temperature and viscosity. Two additional 'mantle-like' models were built up with extra strong temperature-dependent viscosity to imitate the flow in the Earth's mantle. In model 1, in which the viscosity decreases seven orders of magnitude with the temperature increase, a highly viscous stagnant lid evolves along the cold surface which does not participate in the convection. The existence of the stagnant surface lid reduces the surface heat flow and generates a low viscosity asthenosphere beneath the lid with vigorous small-scale convection. In model 2, in which the viscosity decreases only six orders of magnitude with the temperature and the pressure-dependent viscosity is stronger, does not form a surface stagnant lid, highly viscous 'slabs' submerge to the CMB and effectively influence the hot upwelling plumes. Based on our numerical results it is necessary to implicate the yield stress into the simulations in order to obtain a highly viscous, 'rigid' surface lid, the lithosphere which can be broken up and subduct down to the mantle.
