Unique temperature distribution and explicit efficiency formula for one-dimensional thermoelectric generators under constant Seebeck coefficients

A thermoelectric generator converts a temperature difference into electrical energy. Its energy conversion efficiency is determined by the steady-state temperature distribution inside the generator. By assuming the thermoelectric material in the generator has a temperature-independent Seebeck coefficient and the generator is one-dimensional, we show that the second-order integro-differential equation describing the inside temperature distribution has a unique solution for any given ratio of external load resistance to the internal resistance. Hence the efficiency is well defined. Furthermore, we show the efficiency has an explicit formula in terms of the temperature-dependent thermal conductivity and electrical resistivity of the thermoelectric material. On the contrary, the integro-differential equation may have multiple solutions if an external load resistance value is given instead of the external-load-to-internal resistance ratio.(c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

A thermoelectric generator's energy conversion efficiency is determined by the steady-state temperature distribution, which can be solved by a second-order integro-differential equation with a unique solution. The efficiency can be calculated using the temperature-dependent thermal conductivity and electrical resistivity of the thermoelectric material.