Thermoelectric generators (TEGs) are being studied and developed for applications in which waste heat, for example, from the exhaust of motor vehicles is converted into usable electricity. TEGs consisting of TE elements integrated with an exhaust heat exchanger require optimization to produce the maximum possible power output. Important optimization parameters include TE element leg length, fill fraction, leg area ratio between n- and p-type legs, and load resistance. A finite difference model was developed to study the interdependencies among these optimization parameters for thermoelectric elements integrated with an exhaust gas heat exchanger. The present study was carried out for TE devices made from n-type Mg(2)si and p-type MnSi1.8 based silicides, which are promising TE materials for use at high temperatures associated with some exhaust heat recovery systems. The model uses specified convection boundary conditions instead of specified temperature boundary conditions to duplicate realistic operating conditions for a waste heat recovery system installed in the exhaust of a vehicle. The 1st generation, and an improved 2nd generation TEG module using Mg2Si and p-type MnSi1.8 based silicides were fabricated and tested to compare TE power generation with the numerical model. Important results include parameter values for maximum power output per unit area and the interdependencies among those parameters. Heat transfer through the void areas was neglected in the numerical model. When thermal contact resistance between the TE element and the heat exchangers is considered negligible, the numerical model predicts that any volume of TE material can produce the same power per unit area, given the parameters are accurately optimized. Incorporating the thermal contact resistance, the numerical model predicts that the peak power output is greater for longer TE elements with larger leg areas. The optimization results present strategies to improve the performance of TEG modules used for waste heat recovery systems. (C) 2014 Elsevier Ltd. All rights reserved.