Dimensionless Model of a Thermoelectric Cooling Device Operating at Real Heat Transfer Conditions: Maximum Cooling Capacity Mode

Abstract

Real operating conditions of a thermoelectric cooling device are in the presence of thermal resistances between thermoelectric material and a heat medium or cooling object. They limit performance of a device and should be considered when modeling. Here we propose a dimensionless mathematical steady state model, which takes them into account. Analytical equations for dimensionless cooling capacity, voltage, and coefficient of performance (COP) depending on dimensionless current are given. For improved accuracy a device can be modeled with use of numerical or combined analytical-numerical methods. The results of modeling are in acceptable accordance with experimental results. The case of zero temperature difference between hot and cold heat mediums at which the maximum cooling capacity mode appears is considered in detail. Optimal device parameters for maximal cooling capacity, such as fraction of thermal conductance on the cold side y, fraction of current relative to maximal j′ are estimated in range of 0.38–0.44 and 0.48–0.95, respectively, for dimensionless conductance K′ = 5–100. Also, a method for determination of thermal resistances of a thermoelectric cooling system is proposed.