Understanding Thermal Lagging Behaviors in Thermoelectric Elements with the Dual-Phase-Lag Model

Abstract

This study investigates the heat transport mechanism in semiconductor elements within a homogeneous thermoelectric cooling system using the dual-phase-lag model. The thermal lagging behavior is analyzed and explored during the energy transport process. The coupled energy and constitutive partial differential equations are solved simultaneously to reduce the complexity of the high-order spatial and time derivatives. This approach simplifies the mathematical solution process and reduces numerical instabilities when compared to the conventional methodology in which either the temperature or heat flux are solved individually with a single equation. The effect of the thermal lagging behavior on energy transport is examined and compared to results by using the Cattaneo-Vernotte model. Furthermore, the phase-lag behavior on the temperature and heat flux profiles are investigated in detail. This study provides perceptive information for engineering applications in which microscale heat transport phenomenon plays a significant role during the design process. Adding the dual-phase-lag model to the traditional heat diffusion model will be a complementary option for engineers in the thermoelectric industry.