Abstract
The efficiency of a thermoelectric (TE) generator for the conversion of thermal energy into electrical energy can be easily but roughly estimated using a constant properties model (CPM) developed by Ioffe. However, material properties are, in general, temperature ()-dependent and the CPM yields meaningful estimates only if physically appropriate averages, i.e., spatial averages for thermal and electrical resistivities and the temperature average (TAv) for the Seebeck coefficient (, are used. Even though the use of compensates for the absence of Thomson heat in the CPM in the overall heat balance, we find that the CPM still overestimates performance (e.g., by up to 6% for PbTe) for many materials. The deviation originates from an asymmetric distribution of internally released Joule heat to either side of the TE leg and the distribution of internally released Thomson heat between the hot and cold side. The Thomson heat distribution differs from a complete compensation of the corresponding Peltier heat balance in the CPM. Both effects are estimated quantitatively here, showing that both may reach the same order of magnitude, but which one dominates varies from case to case, depending on the specific temperature characteristics of the thermoelectric properties. The role of the Thomson heat distribution is illustrated by a discussion of the transport entropy flow based on the plot. The changes in the lateral distribution of the internal heat lead to a difference in the heat input, the optimum current and thus of the efficiency of the CPM compared to the real case, while the estimate of generated power at maximum efficiency remains less affected as it is bound to the deviation of the optimum current, which is mostly <1%. This deviation can be corrected to a large extent by estimating the lateral Thomson heat distribution and the asymmetry of the Joule heat distribution. A simple guiding rule for the former is found.
Highlights
Thermoelectric generator (TEG) materials convert a certain fraction of the heat passed through them into useful electrical power, as the charge carriers absorb the thermal energy and move from the hot side to the cold side, carrying entropy [1,2]
From the study of 2TD and 1TD model materials with one or two selected properties among α, ρ and κ set as constant, which results in both redistribution of heat between the hot and cold side of the element and the change of spatial averages, we see that in some examples, large deviations in efficiency δηmodel max arise as a consequence of considerable modification of the T profile
In comparison to the efficiency deviation between the constant properties model (CPM) and real materials δηmax which conserve the spatial property averages and are mostly below 2%, this shows that a change of spatial averages due to an arbitrary modification of the T profile may contribute a strong shift to the efficiency estimate
Summary
Thermoelectric generator (TEG) materials convert a certain fraction of the heat passed through them into useful electrical power, as the charge carriers (holes/electrons) absorb the thermal energy and move from the hot side to the cold side, carrying entropy [1,2]. ∂x local Thomson heat absorption driven by the change of the convective entropy flux αj related to the temperature dependence of α(T ), and ρ(T ) j2 corresponds to the local Joule heat dissipation. We explain the physical origin of a relevant part of the discrepancy between CPM results and the real situation using a schematic plot of the convective entropy flux derived from an α(T ) graph, alongside showing that the net Peltier/Thomson heat is correctly considered by the CPM when appropriate temperature averaging is used for α(T ). Marked areas in the entropy flux diagram quantify the exchange of Peltier and Thomson heat, and with that, a correction for the related deviation in CPM efficiency estimation, dηmax =
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
