Compatibility factor for the power output of a thermogenerator

The compatibility approach introduced by Snyder and Ursell enables the description of both thermoelectric generator (TEG) and Peltier cooler (TEC) within the framework of a unified ID model. Both TEG's efficiency ν and TEC's coefficient of performance (C.O.P.) can be formulated in terms of the reduced current density u, which has been introduced as a new, intensive state variable of a thermoelectric system. For ν and C.O.P., integral expressions are formed from additive contributions of all length segments of a thermoelectric element, enabling exact calculation of these quantities even for arbitrarily graded elements. Maximization of these global performance parameters can thus be deduced to local maximization. Here the maximum power from a TEG with fixed length but variable heat supply is considered, which leads to the new concept of power-related compatibility and to the introduction of a new, different compatibility factor.