Implementing third-order discriminant for feasibility analysis in thermoelectric cooling designs

Designing efficient thermoelectric cooling systems (TCS) to meet specific thermal management requirements is a complex engineering challenge that often requires specialized knowledge and extensive computational resources. This study presents an innovative method for evaluating the feasibility of a TCS in maintaining the required surface temperature while dissipating a specified amount of heat under defined environmental conditions. The proposed method utilizes non-dimensionalization and is fully analytical. The third-order discriminant of the expression for the cold-side temperature is proposed in this study for the first time as a criterion for feasibility. The proposed criterion enables not only the assessment of whether a given TCS is capable of meeting its specified goals, but also the inverse problem: performing an analytical calculation of the TCS parameters required to achieve the desired cooling performance across various operating scenarios. The method returns the values of the calculated parameters in the standard format used by TEC manufacturers. Using this criterion streamlines the design of thermoelectric cooling systems for various applications, such as minimizing the temperature of the cooled surface, reducing the system’s cost and volume under constant thermal load, and selecting components for a system with closed-loop dynamic temperature control, among others. The study also presents, for visualization, an original graphical representation of the dimensionless analysis, as well as a graphical interpretation of the feasibility region, allowing one to assess the proximity of the requirements for the maintained temperature and dissipated heat to the feasibility boundary and to evaluate the system’s robustness. Experimental validation demonstrates that the proposed method is practically applicable.