Optimal design of thermoelectric devices with dimensional analysis

The optimum design of thermoelectric devices (thermoelectric generator and cooler) in connection with heat sinks was developed using dimensional analysis. New dimensionless groups were properly defined to represent important parameters of the thermoelectric devices. Particularly, use of the convection conductance of a fluid in the denominators of the dimensionless parameters was critically important, which leads to a new optimum design. This allows us to determine either the optimal number of thermocouples or the optimal thermal conductance (the geometric ratio of footprint of leg to leg length). It is stated from the present dimensional analysis that, if two fluid temperatures on the heat sinks are given, an optimum design always exists and can be found with the feasible mechanical constraints. The optimum design includes the optimum parameters such as efficiency, power, current, geometry or number of thermocouples, and thermal resistances of heat sinks.