Derivation of generalized thermoelectric energy equations and the study of thermoelectric irreversible processes based on energy, exergy, and entransy analysis

Thermoelectric (TE) generation is becoming a valuable and promising research direction. Many researchers have carried out system analysis and performance optimization of thermoelectric technologies based on the generalized thermoelectric energy balance equations. However, it is assumed that TE legs have no heat exchange with the ambient except at the junctions of the hot and cold ends where heat flows in and out. Based on basic thermoelectric effects and fundamental theories of heat transfer, a detailed derivation of the revised generalized thermoelectric energy equations considering convective heat transfer between TE legs and the ambient has been carried out. Irreversible heat transfer processes have been analyzed by employing energy analysis based on the first law of thermodynamics and exergy analysis based on the second law of thermodynamics. The results show that convective heat transfer leads to a decrease in both energy and exergy efficiencies: the rate and magnitude of the decrease in exergy efficiency are greater than those of the decrease in energy efficiency. The exergy efficiency is relatively high despite the low energy efficiency in operation, revealing the features and advantages of thermoelectric generators (TEGs) in low-grade energy utilization. For TEG efficient operation, the load resistance value should match the system's internal resistance, or at least be greater than that, to avoid a sharp drop in power output and efficiencies. In an attempt at theoretical analysis, the concept of entransy was first introduced into thermoelectric analysis, yielding two concise relational equations which reflect the intrinsic link between Carnot cycle efficiency, energy efficiency, exergy efficiency, and entransy flow transfer efficiency. The entransy analysis based on the index of entransy flow transfer efficiency, together with energy analysis and exergy analysis, may be a novel and valuable guideline for the operation and optimization of TEGs, which needs to be further investigated. Schematic representation of a pair of thermoelectric legs.image