Analysis of a hybrid thermoelectric microcooler: Thomson heat and geometric optimization

In this work, we analyze the thermodynamics and geometric optimization of thermoelectric elements in a hybrid two-stage thermoelectric micro cooler (TEMC).We propose a novel procedure to improve the performance of the micro cooler based on optimum geometric parameters, cross sectional area (A) and length (L), of the semiconductor elements. Our analysis takes into account the Thomson effect to show its role on the performance of the system. We obtain dimensionless temperature spatial distributions, coefficient of performance (COP) and cooling power (Q_c) in terms of the electric current for different values of the geometric ratio ω = A/L. In our analysis we consider two cases: (a) the same materials in both stages (homogeneous system); and (b) different materials in each stage (hybrid system).We introduce the geometric parameter, W = ω₁/ω₂, to optimize the micro device considering the geometric parameters of both stages, ω₁ and ω₂. Our results show the optimal configuration of materials that must be used in each stage. The Thomson effect leads to a slight improvement on the performance of the micro cooler. We determine the optimal electrical current to obtain the best performance of the TEMC. Geometric parameters have been optimized and results show that the hybrid system reaches a maximum cooling power 15.9% greater than the one-stage system (with the same electric current I = 0.49 A), and 11% greater than a homogeneous system, when ω = 0.78. The optimization of the ratio in the number of thermocouples in each stage shows that (COP) and (Q_c) increase as the number of thermocouples in the second stage increase too, but with W = 0.94. We show that when two materials with different performances are placed in each stage, the optimal configuration of materials in the stages of the system must be determined to obtain a better performance of the hybrid two-stage TEMC system. These results are important because we offer a novel procedure to optimize a thermoelectric micro cooler considering the geometry of materials at a micro level.