Analyses of cost of energy and multi-objective optimizations for single-stage thermoelectric coolers

Abstract

Abstract Based on finite-time thermodynamics and single-stage thermoelectric cooler model from prior literature, this study introduces the cost of energy, it is defined as COE = Q L / I , which quantifies heat flux per unit current passing through thermoelectric cooler from cold end, and fills a gap in finite-time thermodynamics as a new thermodynamic index. The cost of energy expression is derived, and the current and area allocation of heat-exchangers are optimized to maximize the cost of energy under fixed total heat-exchanger area. Using NSGA-II, 1- to 4-objective optimizations are performed for cooling load, coefficient of performance, efficient cooling load and cost of energy. TOPSIS, LINMAP and Shannon Entropy methods are used to identify optimal solutions. The maximum cost of energy increases with the thermoelectric unit number and total heat transfer area, but decreases with heat reservoir temperature difference. When external heat-transfer loss is considered, the maximum cost of energy decreases by 22.1 %. For four-objective optimization, the optimal current is distributed between 5 A and 40 A, and optimal heat-exchanger area allocation ratio ranges from 0.5 to 0.63 and clusters mainly between 0.55 and 0.6. Key contributions are cost of energy analysis and four-objective optimization for single-stage thermoelectric cooler by using finite-time-thermodynamics and multi-objective methods.