A numerical simulation of a turbulent flow of water in three shell and tube heat exchangers equipped with 6, 8, 10 segmental baffles as the working fluid at Reynolds numbers ranging from 24327, 33356, 42569 are performed. The conservation equations of mass, momentum and energy are solved by the finite volume method based on the SIMPLE algorithm for coupling velocity-pressure, the mathematical model k-ε within the Fluent software is used in the different cases presented. The temperature, the velocity, the friction factor, the heat transfer coefficient, the pressure drop in the shell, the total heat transfer rate between the tubes and the fluid, the overall performance factor are studied for the three spacing between baffles. This work contributes largely to the understanding of turbulent flows and also shows the effect of the baffles number on the heat transfer in the heat exchangers. The velocity of flow in the shell increases by 1.49% and 1.62% and 1.73% of the reference velocity. The results show an increase in the outlet temperature, heat transfer coefficient 1.09% and 1.28%, pressure drop 1.7% and 2.82%, the total heat transfer rate 1.08% and 1.18% because of the increase in number of baffles. The results obtained in this study are in good agreement and correspond to the results given by the literature.