Generalized analytic one-dimensional description of non-homogeneous TE cooler and generator elements based on the compatibility approach

Graded and segmented thermoelements have been considered for long, aiming at improving the performance of thermogenerators (TEGs) which are exposed to a large temperature difference. Proof was given recently that thermoelectric material gradients exert an essential influence also on the performance of Peltier coolers (TECs) [Muller, et al., 2006, Muller, et al., 2005]. The results of the continua-theoretical solution describing stacked thermoelectric pellets and their optimization of performance [Muller, et al., 2006] are complemented here by an analytic approach related to the relative current density u(T) which opens a new temperature-based approach to the optimization of non-homogeneous TE devices. This concept (compatibility approach) was first introduced for TEGs by Snyder and Ursell [Snyder, et al., 2003]. They succeeded in deducing a differential equation for u(T) which is enabling the calculation of the reduced efficiency eta_r(T) as a local variable of state, leading finally to the description of the overall efficiency as a function of the electric current density. This work shows that the compatibility approach can be generalized and applied also to the Peltier cooler case. Most obvious analogy in the formal description is achieved with referring to the heat absorbing side (which is the cold side of the cooler but the hot side of the TEG, respectively) and the sink side. TEG and TEC cases are then mainly distinguished by reversal of the temperature difference, with typically much larger optimal current density for the cooler than for the generator. Limitations of this description and first results will be discussed