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The geomagnetic field is generated by the dynamo processes in the liquid core of the Earth. Currently convection has at least two counterparts: the thermal convection due to the cooling of the core, and the compositional convection. The latter one is concerned with the inner core growth. Evolution of the inner core and the thermal state in the core leads to the change of the basic parameters of the geodynamo. From one point of view appearance of the inner core, which accordingly to the models of the thermal evolution of the core took place 1-2Gy ago, can not remain undetected. However paleomagnetic observations do not support this scenario. Firstly, the geomagnetic field was observed early before the start of the inner core nucleation, at least 3.6Ga. Secondly, the proposed by the thermal evolution models age of the inner core does not correlate to any significant change of the paleomagnetic field. We try to examine this situation, using different scenarios of the thermal history of the core. The model includes cooling of the core, crystallisation of the inner core, appearance of the stable regions with the sub-adiabatic temperature profiles at the core-mantle boundary. In fact one has three adjacent regions with two moving boundaries, corresponding to the growing inner core and extending sub-adiabatic region, where the state is governed by the different equations. The model gives distribution of the temperature, thermal fluxes, as well as the coordinates of the boundaries. To resolve these quantities the physical state's parameters: density, pressure, gravity, temperature of the melting are recalculated at every time step. Using this information as well as information on evolution of the day's length one can estimate evolution of the dimensionless parameters of the dynamo equations, such as: the Ekman, thermal and compositional Rayleigh numbers. In its turn, using the scaling laws, these numbers can be related to the dynamic parameters: the Rossby and hydrodynamic Reynolds numbers. Finally, the latter parameter can be converted to the magnetic Reynolds number. Information on the mentioned parameters helps to predict evolution of the frequency of the magnetic fields reversals, magnetic field intensity, angular variations of the magnetic field near the geographic pole.