Peltier supercooling in transient thermoelectrics: Spatial temperature profile and characteristic cooling length

Thermoelectric coolers (TECs) can reach temperatures below that obtained with a steady-state current by applying an electrical current pulse which enables a transitory state in a Peltier device. This effect is known as supercooling. In this paper, we study characteristics parameters, such as the minimum cooling temperature and spatial temperature profile, in a TEC operated under current pulses and a cooling load (Q_c). Numerical analysis for a one-dimensional thermoelectric model of the cooling system is developed, and a novel MATLAB programming code is proposed for the transient state based on finite element analysis. We also investigate the influence of the thermoelement's length upon the cooling mechanism. A new parameter called the "characteristic cooling length" is proposed to describe the length in which the minimum cooling temperature occurs along the elements of a TEM. Results show the transient temperature profiles along the elements of the semiconductor P-type element, and a "characteristic cooling length" is characterized. We also propose a general principle, and the lowest cooling temperature values are obtained for a semiconductor's small length and variable pulse cooling load under current pulse operation. The present study will serve as guidance for the geometric design of TECs under current pulse operations.