Application of the Thermal Quadrupole Method in the Characterization of Thermoelectric Modules
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Application of the Thermal Quadrupole Method in the Characterization of Thermoelectric Modules Euripides Hatzikraniotis, Ioannis Samaras, Dimitra Georgakaki, and Konstantinos M Paraskevopoulos Dept. of Physics, Aristotle University of Thessaloniki, Section of Solid State Physics, University Campus, Thessaloniki, GR 54124, Greece ABSTRACT Measurements of assembled thermoelectric (TE) modules commonly include investigations of the module output power versus load resistance. Using an AC electrical measurement for TE modules, a model of equivalent passive RC circuit has been developed and tested for both the thermal and electrical characteristics of the module. In this work we present and analyze data of a commercially available module, using equivalent passive RC circuit, to examine, explain and model the electro-thermal activity in the module. In addition data we analyzed by thermal quadrupole theory. Measurements were taken over the frequency range of 0,5mHz to 50 Hz. INTRODUCTION A thermoelectric (TE) module is an active device. Such a device consists of an array of pellets from dissimilar semiconductor material (p and n type) joined electrically in series and thermally in parallel, contained between ceramic end caps (TE module). The metallized connecting bars on ceramic plate serve to connect all of the couples in series. Applying a DC voltage source across the input terminals of the device causes a temperature gradient that subsequently develops a voltage due to the Seebeck effect. This voltage is equal to the Seebeck coefficient, α, multiplied by the temperature gradient, ∆Τ. In steady state the electro-thermal behavior of the module is described by the Harman technique [1]. In the Harman method, a square wave electric current feeds the sample, and the sample voltage V can be written: 2 ⎡a ⋅T ⎤ α 2 ⋅T d d ⋅ ⋅ I + ρ ⋅ I = VR ⎢ − 1⎥ (1) V = VSeebeck + V R = κ S S ⎣κ ⋅ρ ⎦ where d and S are the thickness and the cross section of the sample, T is the average temperature, ρ is the electrical resistivity and κ is the thermal conductivity. In the harmonic method a pure sine wave electric current flows through the sample. There have been research studies for both DC [2] and AC [3-5] electrical measurements and modeling of TE modules. Recently, Dilhare et al [6-8] have developed a method, the thermal quadropole theory, according to which the thermoelectric properties should be extracted individually, from a sole set of measurements. The method is based on the harmonic regime response analysis of a sample mounted in the typical "suspended sample" configuration as used in the Harman method. In this approach, the heat transfer problem is solved for a pure sine wave excitation current through the sample, by means of the thermal quadrupoles method. Despite the non-linear nature of thermoelectric phenomena, it is shown that an AC harmonic analysis is possible, without any loss of accuracy.
In this paper we present an analysis of a TE device in AC response, both in frequency and time domain, which can be modeled us
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