The aim of this work is numerical modeling of the hydrodynamics and heat transfer of a shell-and-tube heat exchanger. For the purpose of the study a 3D model with geometric dimensions corresponding to real was created. The simulations under the same boundary conditions as experiment were carried out. The independence of solution by the density and the shape of the mesh were investigated. For verification the experimental values for fluid temperatures at the outlets from the apparatus were used. The simulations of different operation modes in the apparatus were carried out. A modification in the geometry with the aim of raising the temperature on the cold fluid at the outlet was made. Results on vectors, velocity and temperature distribution in the apparatus were obtained. On the basis of the obtained results some design changes of the apparatus in order to improve the hydrodynamics have been proposed. The obtained results can be successfully used in the design, optimization and constructing of this type apparatus, as well as in the educational process.