When the thermoelectric generator (TEG) modules are attached to a larger chimney plate, the power generated per unit surface area (power density) is strongly dependent on the TEG module spacing. The thermoelectric module consists of a hot plate, a spreader, a thermoelectric generator and a cold plate based on water cooling. In the study, a three-dimensional thermoelectric generator heat transfer-electricity model is proposed and solved numerically using the finite difference method along with a simplified conjugate-gradient method. The power density for thermoelectric module is the objective function to be maximized. A search for the optimum module spacing (S) and spreader thickness (Hsp), ranging from 40 mm S 300 mm and 1 mm Hsp 30 mm, respectively, is performed. The effects of different operating conditions, including cooling water heat transfer coefficients (500 - 2000 W/m 2·K ), waste gas heat transfer coefficients ( 20 - 80 W/m 2·K ) are investigated and discussed in detail.