Dimensionless Mathematical Model of a Thermoelectric Cooler: ΔTmax Mode

Abstract

The thermal resistances on the cold and hot sides substantially affect the output characteristics of thermoelectric devices. A dimensionless mathematical model of a thermoelectric cooler, which makes it possible to calculate device parameters, such as the optimal thermal resistance ratio on the cold and hot sides as well as the optimal current taking into account the influence of thermal resistances, is presented. The maximal temperature difference ΔT_max mode is considered. It is shown that the optimal cooler parameters are different for implementation of the ΔT_max and Q_max modes. The determining factor for the ΔT_max mode is the influence of the thermal resistance on the hot side, and the optimal current is 0.4–0.7 of the maximal current in most cases for the material with ZT = 1. It is shown that an additional increase in ΔT_max of a cooler is attained with a decrease in the thermal conductivity of the thermoelectric material due to a decrease in the influence of the thermal resistance on the hot side besides the effect from an increase in ZT. An increase in the length of thermoelectric legs has the same positive effect of an increase in ΔT_max of a cooler, while a decrease in the leg length negatively affects ΔT_max.