Critical analysis on the suitability of a Constant Properties Model (CPM) for performance analysis of thermoelectric generators

A thermoelectric generator (TEG) consists of a series of p-n semiconductor leg pairs electrically connected in series and thermally in parallel, and converts thermal energy to electrical energy, serving as a potential solution to meet increasing energy demands by harvesting energy from waste heat. Accurate performance analysis of TEGs requires solving the Domenicali’s thermoelectric heat balance equation, which is a second order nonlinear partial differential equation with non-constant coefficients, numerically solvable by Finite Element Methods (FEM). Since FEM is costly and time consuming, an approximate model assuming constant material properties suggested by Ioffe is widely used. However, the thermoelectric (TE) material properties are temperature (T ) dependent in general, and the Constant Properties Model (CPM) can yield meaningful estimates only if the constant values (obtained by averaging the T  dependent data) are physically appropriate. The question of the effect of selecting an appropriate averaging method has not been exhaustively discussed yet. Additionally, the magnitude of remaining uncertainty when using CPM for TEG performance calculations has not been of much focus in the TE literature. Therefore, this thesis deals with this aspect in larger detail at various levels, focussing on the device aspect but also linking module to material optimization.

Initially, by comparing different averaging modes we demonstrate that a combination of integral averaging over the temperature scale for the Seebeck coefficient and spatial averages (integration over length) for the electrical and thermal resistivities proves to be the best to represent the constant property values. We show that the still remaining deviation due to uncompensated Thomson heat can be corrected using a simple entropy flow diagram. Further, using a material-device model developed in-house, we not only show that the material figure of merit zT , based on CPM, can be misleading in the search for optimum material parameters (such as carrier concentration), but we also demonstrate the usefulness of this tool in studies such as functional material grading.  

In summary, this research work provides useful insights about the usage of CPM which is most commonly used in thermoelectrics, clarifying wide spread misconceptions, as well as providing faster and efficient tools for performance calculation and for accurate material optimization.



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