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A thermo-hydrodynamic neutron interaction model for permanent working conditions is developed in the case of closed circuits (boiling water reactors) and open circuits (pressurized water reactors). Two numerical convergence acceleration methods are then worked out for the resolution of linear problems by successive iterations. A physical study is devoted to the convergence of the thermo-hydrodynamic neutron interaction process. The model developed is applied to the calculation of the power distribution for the core of a 980 MWe BWR-6 type boiling water power station and to the study of normal and accidental working configurations of the pressurized water core of a 900 MWe PWR-CP1 unit. (Atomindex citation 11:514211)