A Study of the Nonlinear Thomson Effect Produced by Changing the Current in a Thermoelectric Cooler

Abstract

Abstract This work describes the nonlinear Thomson effect produced by a transient current source powering a thermoelectric cooler. The electric effect of the capacitive impedance in the semiconductors was considered in the equations as a novelty term that naturally appears by solving the Boltzmann equation to find the mathematical form of the current density. Thus, considering the new term and heath energy balances, a one-dimensional mathematical model for a thermoelectric cooler (TEC) powered by a time-dependent current was developed, finding a new nonlinear Thomson effect in the heath transfer equations. To evaluate the impact of the nonlinear effect on the thermodynamic behavior of the thermoelectric cooler, a continuous, sinusoidal and square-pulse current conditions were simulated. The temperature profile, temporal evolution, and the effective coefficient of performance (COP) were calculated. The results revealed a new thermoelectric heat transfer in addition to the Thomson flow created by virtual junctions throughout the semiconductors caused by the instantaneous change of current. This fact was evidenced by three results: the shifting of the temperature mean value due to the peak current change 0.45 A is 1.68 K 1.68\hspace{0.1667em}\mathrm{K} and 2.56 K 2.56\hspace{0.1667em}\mathrm{K} to sinusoidal and square current supplies, respectively; it was determined that a TEC powered by a square-pulse current signal had greater effective efficacy, having more pronounced cold side supercooling temperature peaks compared to those powered by a constant sinusoidal current signal.