Temperature gradient characteristics and effect on optimal thermoelectric performance in exhaust power-generation systems

•A nonisothermal thermoelectric model is developed using the finite element method.•Temperature gradient at different work conditions is shown by fitting correlations.•Thermoelectric material properties’ temperature dependence is considered.•An effective finite element calculation method is obtained with high precision.•It is feasible to take one thermoelectric module as one finite calculation element. An obvious temperature gradient is apparent when engine exhaust gas with low mass flow and a high temperature passes through a thermoelectric generator system to recover thermal energy. Aiming to explore the temperature gradient characteristics and its effect on optimal thermoelectric performance in an exhaust power-generation system, a nonisothermal thermoelectric numerical model was developed using the finite-element method. A commercial-type thermoelectric material was used in the numerical calculation. When the maximum net power was obtained, the corresponding temperature-gradient characteristics under different exhaust mass flow rates and temperatures were examined for an exhaust power-generation system. Moreover, the optimal structural dimensions and maximum net power were investigated with consideration of the temperature dependence of the physical properties of the thermoelectric materials. Additionally, different finite-element conditions were compared to obtain an effective calculation method. The results indicated that the temperature gradient is significantly affected by the exhaust temperature but not the mass flow rate and a linearly increases with an exhaust temperature increase by introducing fitting correlations. Constant physical thermoelectric parameters can be used when the qualitative operating temperature of the semiconductor material is suitably chosen. It is recommended to use one commercial thermoelectric module as one finite calculation element instead of using one PN couple, because this facilitates convenient and high-precision calculations.