Thermal analysis of thermoelectric active cooling including external thermal resistances

Thermoelectric active cooling uses nontraditional thermoelectric materials with high thermal conductivity, high thermoelectric power factor, and relatively low figure of merit (ZT) to transfer large heat flows from a hot object to a cold heat sink. However, prior studies have not considered the influence of external thermal resistances associated with the heat sinks or contacts, making it difficult to design active cooling thermal systems or compare the use of low-ZT and high-ZT materials. Here, we perform a non-dimensionalized analysis of thermoelectric active cooling under forced heat flow boundary conditions, including arbitrary external thermal resistances. We identify the optimal electrical currents to minimize the heat source temperature and find the crossover heat flows at which low-ZT active cooling leads to lower source temperatures than high-ZT and even ZT→+∞ thermoelectric refrigeration. These optimal parameters are insensitive to the thermal resistance between the heat source and thermoelectric materials, but depend strongly on the heat sink thermal resistance. Finally, we map the boundaries where active cooling yields lower source temperatures than thermoelectric refrigeration. For currently considered active cooling materials, active cooling with ZT < 0.1 is advantageous compared to ZT→+∞ refrigeration for dimensionless heat sink thermal conductances larger than 15 and dimensionless source powers between 1 and 100. Thus, our results motivate further investigation of system-level thermoelectric active cooling for applications in electronics thermal management.