Influence of convection at outer ceramic surfaces on the characterization of thermoelectric modules by impedance spectroscopy

Abstract

Impedance spectroscopy is a useful method for the characterization of thermoelectric (TE) modules. It can determine with high accuracy the module's dimensionless figure of merit (zT) as well as the average TE properties of the module's thermoelements. Interpretation of impedance results requires the use of a theoretical model (equivalent circuit), which provides the desired device parameters after a fitting is performed to the experimental results. Here, we extend the currently available equivalent circuit, only valid for adiabatic conditions, to account for the effect of convection at the outer surface of the module ceramic plates, which is the part of the device where convection is more prominent. This is performed by solving the heat equation in the frequency domain including convection heat losses. As a result, a new element (convection resistance) appears in the developed equivalent circuit, which starts to influence at mid-low frequencies, causing a decrease of the typically observed semicircle in the impedance spectrum. If this effect is not taken into account, an underestimation of the zT occurs when measurements are performed under room conditions. The theoretical model is validated by experimental measurements performed in a commercial module with and without vacuum. Interestingly, the use of the new equivalent circuit allows the determination of the convection heat transfer coefficient (h), if the module's Seebeck coefficient is known, and an impedance measurement in vacuum is performed, opening up the possibility to develop TE modules as h sensors. On the other hand, if h is known, all the properties of the module (zT, ohmic (internal) resistance, average Seebeck coefficient and average thermal conductivity of the thermoelements and thermal conductivity of the ceramics) can be obtained from one impedance measurement in vacuum and another measurement under room conditions.