Optimization of supercooling effect in nanoscaled thermoelectric layers

In this paper we address the problem of optimization of the so called supercooling effect in thermoelectric nanoscaled layers. The effect arises when a short term electric pulse is applied to the layer. The analysis is based on constitutive equations of the Maxwell-Cattaneo type describing the time evolution of dissipative flows with the thermal and electric conductivities depending on the width of the layer. This introduces memory and nonlocal effects and consequently a wave-like behaviour of system’s temperature. We study the effects of the shape of the electric pulse on the maximum diminishing of temperature by applying pulses of the form t^a with a a power going from 0 to 10. Pulses with a a fractionary number perform better for nanoscaled devices whereas those with a bigger than unity do it for microscaled ones. We also find that the supercooling effect is improved by a factor of 6.6 over long length scale devices in the best performances and that the elapsed supercooling time for the nanoscaled devices equals the best of the microscaled ones. We use the spectral methods of solution which assure a well representation of wave behaviour of heat and electric charge in short time scales given their spectral convergence.