Performance analysis of multi-stage thermoelectric coolers

Multi-stage thermoelectric coolers offer larger temperature differences between heat source and heat sink than single-stage thermoelectric coolers. In this paper, a pyramid-type multi-stage cooler is analyzed, focusing on the importance of maximum attainable target heat flux and overall coefficient of performance, COP. Having considered the COP and the thermal resistance of a heat sink as key parameters in the design of a multi-stage thermoelectric cooler, analytical formulas for COP and heat sink thermal resistance versus working electrical current are derived. For a fixed cooling target heat flux, the ratio of the heat sink thermal resistance to the respective single-stage value and the attainable COP in a cascaded cooler are determined as a function of the number of stages. Numerical simulations clearly indicate that the thermal resistance of the hot side heat sink is the controlling factor in determining the overall performance of a multi-stage thermoelectric cooler.