Multivariable optimization of two-stage thermoelectric refrigerator driven by two-stage thermoelectric generator with external heat transfer

The finite time thermodynamic model of a combined thermoelectric device, two-stage thermoelectric refrigerator driven by two-stage thermoelectric generator with heat transfer irreversibility is built by combining non-equilibrium thermodynamic theory with finite time thermodynamics theory. The solution procedure of optimal performance and the corresponding optimal variables are given and the cooling load and COP of the combined thermoelectric device are optimized. The control equation of the combined thermoelectric system is obtained. For fixed total number of thermoelectric elements and fixed total external thermal conductance of the device, the allocations of thermoelectric elements and thermal conductance are optimized for maximum cooling load and COP, respectively. The effects of the heat source temperature of the two-stage thermoelectric generator and the heat source (cooling space) temperature of the two-stage thermoelectric refrigerator on the optimal performance and optimal variables selection are analyzed by detailed numerical examples. The numerical simulation results show that the optimization is necessary and effective. By optimization, the performance is improved. When the two-stage thermoelectric generator works at a difference of 150 K, a cooling temperature difference of about 60 K could be reached. When the two-stage thermoelectric refrigerator works at a difference of 20 K, a COP of about 0.10 could be reached. These are considerable for application in a wide-scale for specific purposes.