Optimizing the electrical power output of a thermogenerator with the Gerstenmaier/Wachutka approach

Gerstenmaier and Wachutka have published in PRE 86, 056703 (2012) a new approach (in this paper denoted as G/W approach) to optimizing the material grading in thermoelectric (TE) converters by means of a generalized Lagrange multiplier method. This powerful method allows considering all relevant performance maximization problems within both the “x‐domain” and the “T‐domain”; in the latter case the compatibility approach has been recovered by independent proof. Here, we adapt the G/W approach to optimizing spatial TE material profiles in order to get maximum electrical power output of a graded thermogenerator with fixed length. The new findings are compared with results previously published. This particularly applies the comparison of the optimal Seebeck coefficients for maximum efficiency and maximum power output.