Effect of heat transfer on the performance of a thermoelectric heat pump driven by a thermoelectric generator

A model of a thermoelectric heat pump driven by a thermoelectric generator with external heat transfer irreversibility is proposed. The performance of the combined thermoelectric heat pump device obeying Newton's heat transfer law is analyzed using the combination of finite time thermodynamics and non-equilibrium thermodynamics. Two analytical formulae for heating load versus working electrical current, and the coefficient of performance (COP) versus working electrical current, are derived. For a fixed total heat transfer surface area of four heat exchangers, the allocations of the heat transfer surface area among the four heat exchangers are optimized for maximizing the heating load and the COP of the combined thermoelectric heat pump device. For a fixed total number of thermoelectric elements, the ratio of the number of thermoelectric elements of the generator to the total number of thermoelectric elements is also optimized for maximizing both the heating load and the COP of the combined thermoelectric heat pump device. The influences of thermoelectric element allocation and heat transfer area allocation are analyzed by detailed numerical examples. The optimum working electrical currents for maximum heating load and maximum COP at different total numbers of thermoelectric elements and different total heat transfer areas are provided, respectively.