Computational study of transverse Peltier coolers for low temperature applications

Transverse thermoelectric effect can be produced artificially by stacking at an angle layers of a thermoelectric material with another material that may or may not be a thermoelectric material. In this exploratory computational study, a new meta-material, comprised of tilted alternating layers of an n-type thermoelectric alloy and a metal, is investigated to gain an understanding of how much cooling can be produced by transverse thermoelectric effect and the conditions under which maximum cooling is attainable. The governing conservation equations of energy and electric current, with the inclusion of thermoelectric effects, are solved on an unstructured mesh using the finite-volume method to simulate a transverse Peltier cooler under various operating conditions. First, the code is validated against experimental data for a n-Bi2Te3–Pb meta-material, and subsequently explored. It is found that intermediate applied currents produce maximum temperature depression (ΔT). Optimum values of the geometric design parameters such as tilt angle and device aspect ratio are also established through parametric studies. Finally, it is shown that the ΔT can be amplified by constricting the phonon (heat) transport cross-section while keeping the electron (current) transport cross-section unchanged—a strategy that cannot be employed in conventional thermoelectric devices where electrons and phonons follow the same path. This makes transverse Peltier coolers particularly attractive for generating large ΔT without multi-stage cascading.