Evaluation and design of thermoelectric cooling system for heat dissipation under given surface load

Thermoelectric cooling is promising for thermal management of electronic devices. In real-world applications, many electronic devices are characterized by given heat loads under a specified limitation of the junction temperature. However, most existing fully analytical models of thermoelectric cooling systems are conducted under constant-temperature boundary conditions, which makes it difficult to describe heat sources with a prescribed constant heat flux directly. To address these limitations, a theoretical framework is proposed for a single-stage thermoelectric cooling system under constant heat-flux boundary conditions, enabling accurate estimation of the minimum heat-source temperature (Th,min) and the maximum coefficient of performance (COP). Based on this framework, analytical formulas for the optimal operating current and the optimal engineering thermoelectric (TE) leg length corresponding to the minimum heat source temperature are derived. The proposed formulas are validated through comparisons with numerical simulations and published experimental data, yielding prediction deviations within ±1.4% and ±3.1%, respectively. Furthermore, under given heat load, target heat source temperature, and external heat transfer conditions, general explicit expressions for the maximum COP and the corresponding optimal engineering TE leg length are established to account for the long-term running cost. Compared with the COP associated with the engineering TE leg length at the minimum heat source temperature, the maximum COP can be enhanced by up to ∼25%. This work provides practical guidance for evaluating optimal performance parameters and for the structural design of thermoelectric cooling systems for electronics thermal management.