In this work, we show a general approach for inhomogeneous composite thermoelectric systems, and as an illustrative case, we consider a dual thermoelectric cooler. This composite cooler consists of two thermoelectric modules (TEMs) connected thermally in parallel and electrically in series. Each TEM has different thermoelectric (TE) properties, namely thermal conductance, electrical resistance and the Seebeck coefficient. The system is coupled by thermal conductances to heat reservoirs. The proposed approach consists of derivation of the dimensionless thermoelectric properties for the whole system. Thus, we obtain an equivalent figure of merit whose impact and meaning is discussed. We make use of dimensionless equations to study the impact of the thermal conductance matching on the cooling capacity and the coefficient of the performance of the system. The equivalent thermoelectric properties derived with our formalism include the external conductances and all intrinsic thermoelectric properties of each component of the system. Our proposed approach permits us changing the thermoelectric parameters of the TEMs and the working conditions of the composite system. Furthermore, our analysis shows the effect of the number of thermocouples on the system. These considerations are very useful for the design of thermoelectric composite systems. We reproduce the qualitative behavior of a commercial composite TEM connected electrically in series.
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