Performance of Thermoelectric Coolers with Boundary Resistance for Different Optimization Criteria

The cooling capacity, efficiency and cooling flux for a single stage thermoelectric cooler, as part of a multistage cooler, is analyzed in this study. The Lagrange Multiplier method is used to develop nonlinear algebraic equations for the optimum condition for different objective functions. The analysis includes the effect of heat leak, thermal boundary resistances with thermal reservoirs and the electric contact resistance at the boundary of the thermoelectric element. The effect of thermal contact resistance and thermal spreading resistance are included in the thermal boundary resistance. In addition to important thermoelectric properties, e.g., the effect of the electric and thermal contact resistances, the thickness of the thermoelectric material and the area aspect ratio of thermoelectric elements on the performance of the thermoelectric cooler at the optimum condition is presented and discussed. The results are presented in terms of non-dimensional variables convenient for system design analysis and performance evaluation.