In this study, an investigation of a new three-dimensional model of thermoelectric generators (TEGs) by using CFD modeling is performed. A solution is presented for the physical model of the TEG module which couples the thermal and electrical models. The solution is carried out by using three-dimensional (3D) numerical solution and User defined function (UDF) of the ANSYS-Fluent software. Then, the 3D model is utilized to study the impact of flow regimes on the performance of the TEG mounted on a chimney wall. Also, the impact of the inlet flow velocity of the hot flow gasses and coolant air inside and outside the chimney, respectively on the heat transfer and output power of the TEG is studied. The results show that the present 3D model results agree well with the experimental results compared to the previous models' results. The maximum output power from the TEG modules is obtained when the TEG is installed at the inlet position followed by the turbulent positions of the hot flow gases and cooling air. Increasing the inlet velocity of the hot gases without increasing cooling air velocity or vice versa hasn't great effect on the TEG output power. The heat transfer of the cold side of the TEG is more effective on the TEG output power compared to that of the hot side at the same total flow velocity entering the chimney. To cover only a part of the chimney walls by the TEG modules, and maximize the TEG output power, it is recommended to install the available TEG modules at the chimney wall at the inlet position of the chimney and at the position of the turbulent flow regions inside and outside the chimney.