The influence of Thomson effect in the performance optimization of a two stage thermoelectric cooler

• This paper proposes the exergy analysis in a two stage thermoelectric cooler.
• Analytical expressions for the energy and exergy efficiency in TTEC is derived.
• The influence of Thomson effect in the performance parameters of TTEC is studied.
• The influence of Thomson effect in optimizing the number of thermocouples is studied.

The exoreversible and irreversible thermodynamic models of a two stage thermoelectric cooler (TTEC) considering Thomson effect in conjunction with Peltier, Joule and Fourier heat conduction effects have been investigated using exergy analysis. New expressions for the interstage temperature, optimum current for the maximum cooling power, energy and exergy efficiency conditions, energy efficiency and exergy efficiency of a TTEC are derived as well. The number of thermocouples in the first and second stages of a TTEC for the maximum cooling power, energy and exergy efficiency conditions are optimized. The results show that the exergy efficiency is lower than the energy efficiency e.g., in an irreversible TTEC with total 30 thermocouples, heat sink temperature (TH) of 300 K and heat source temperature (TC) of 280 K, the obtained maximum cooling power, maximum energy and exergy efficiency are 20.37 W, 0.7147 and 5.10% respectively. It has been found that the Thomson effect increases the cooling power and energy efficiency of the TTEC system e.g., in the exoreversible TTEC the cooling power and energy efficiency increased from 14.87 W to 16.36 W and from 0.4079 to 0.4998 respectively for ΔTC of 40 K when Thomson effect is considered. It has also been found that the heat transfer area at the hot side of an irreversible TTEC should be higher than the cold side for maximum performance operation. This study will help in the designing of the actual multistage thermoelectric cooling systems.